{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n c\u00e1c s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["14"],["4"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>\u0110i\u1ec3m s\u1ed1 trung b\u00ecnh c\u1ee7a m\u1ed9t v\u1eadn \u0111\u1ed9ng vi\u00ean b\u1eafn s\u00fang sau $100 $ l\u1ea7n b\u1eafn l\u00e0 $8,69$ \u0111i\u1ec3m . K\u1ebft qu\u1ea3 c\u1ee5 th\u1ec3 \u0111\u01b0\u1ee3c ghi trong b\u1ea3ng sau, trong \u0111\u00f3 c\u00f3 2 \u00f4 b\u1ecb m\u1edd kh\u00f4ng \u0111\u1ecdc \u0111\u01b0\u1ee3c. H\u00e3y t\u00ecm c\u00e1c s\u1ed1 trong hai \u00f4 \u0111\u00f3 r\u1ed3i \u0111i\u1ec1n v\u00e0o.<\/span><br\/><table> <tr> <th>\u0110i\u1ec3m s\u1ed1<br><\/th><td>$10$<\/td> <td>$9$<\/td> <td>$8$<\/td><td>$7$<\/td><td>$6$<\/td> <\/tr> <tr><th>S\u1ed1 l\u1ea7n b\u1eafn<br\/><\/th><td>$25$<\/td><td>$42$<\/td> <td>_input_<\/td><td>$15$<\/td><td>_input_<\/td><\/tr> <\/table>","hint":"\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh \u0111i\u1ec3m s\u1ed1 trung b\u00ecnh \u0111\u1ec3 l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi \u1ea9n l\u00e0 hai \u00f4 tr\u1ed1ng c\u1ea7n \u0111i\u1ec1n<br\/>$X=\\dfrac{{{x}_{1}}{{n}_{1}}+{{x}_{2}}{{n}_{2}}+....+{{x}_{m}}{{n}_{m}}}{{{n}_{1}}+...+{{n}_{m}}}$ trong \u0111\u00f3 <br\/>${{x}_{1}},...,{{x}_{n}}$ l\u00e0 c\u00e1c gi\u00e1 tr\u1ecb \u0111i\u1ec3m, <br\/>${{n}_{1}}$ l\u00e0 s\u1ed1 l\u1ea7n \u0111\u01b0\u1ee3c \u0111i\u1ec3m ${{x}_{1}}$ ,\u2026, ${{n}_{m}}$ l\u00e0 s\u1ed1 l\u1ea7n \u0111\u01b0\u1ee3c \u0111i\u1ec3m ${{x}_{m}}$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>- G\u1ecdi s\u1ed1 c\u1ea7n \u0111i\u1ec1n trong hai \u00f4 tr\u1ed1ng l\u00e0 \u1ea9n. \u0110\u1eb7t \u0111i\u1ec1u ki\u1ec7n cho \u1ea9n.<br\/>- L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb t\u1ed5ng s\u1ed1 l\u1ea7n b\u1eafn<br\/>- L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb \u0111i\u1ec3m s\u1ed1 trung b\u00ecnh c\u1ee7a 100 l\u1ea7n b\u1eafn<br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1<br\/>B\u01b0\u1edbc 3: Ki\u1ec3m tra nghi\u1ec7m v\u00e0 k\u1ebft lu\u1eadn b\u00e0i to\u00e1n<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi hai \u00f4 tr\u1ed1ng c\u1ea7n t\u00ecm t\u01b0\u01a1ng \u1ee9ng v\u1edbi \u0111i\u1ec3m $8$ v\u00e0 \u0111i\u1ec3m $6$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 $x$ v\u00e0 $y$ $(x; y \\in \\mathbb{N})$ <br\/> Do c\u00f3 100 l\u1ea7n b\u1eafn n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: <br\/> $25+42+x+15+y=100\\Leftrightarrow x+y=18$ (1) <br\/> \u0110i\u1ec3m s\u1ed1 trung b\u00ecnh c\u1ee7a m\u1ed9t v\u1eadn \u0111\u1ed9ng vi\u00ean b\u1eafn s\u00fang sau $100$ l\u1ea7n b\u1eafn l\u00e0 $8,69$ \u0111i\u1ec3m n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: <br\/>$\\dfrac{10.25+9.42+8x+7.15+6.y}{100}=8,69\\Leftrightarrow 8x+6y=136\\Leftrightarrow 4x+3y=68$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& x+y=18 \\\\ & 4x+3y=68 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& 4x+4y=72 \\\\ & 4x+3y=68 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& y=4 \\\\ & x+y=18 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& y=4 \\\\ & x=18-y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& y=4 \\\\ & x=14 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n)<br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $14$ v\u00e0 $4.$<\/span><\/span>"}]}],"id_ques":321},{"time":24,"part":[{"time":3,"title":"Hai n\u0103m tr\u01b0\u1edbc tu\u1ed5i c\u1ee7a anh g\u1ea5p ba l\u1ea7n tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi em. Hai n\u0103m sau tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi anh g\u1ea5p hai l\u1ea7n tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi em. H\u1ecfi tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi anh v\u00e0 ng\u01b0\u1eddi em hi\u1ec7n nay ","title_trans":"H\u00e3y s\u1eafp x\u1ebfp c\u00e1c \u00fd \u0111\u1ec3 \u0111\u01b0\u1ee3c l\u1eddi gi\u1ea3i \u0111\u00fang","temp":"sequence","correct":[[[6],[3],[1],[4],[2],[5]]],"list":[{"point":5,"image":"img\/1.png","left":["V\u1eady hi\u1ec7n nay, em $6$ tu\u1ed5i v\u00e0 anh $14$ tu\u1ed5i.","Hai n\u0103m sau, tu\u1ed5i anh l\u00e0 $x+2$, tu\u1ed5i em l\u00e0 $y+2.$ V\u00ec tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi anh g\u1ea5p hai l\u1ea7n tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi em n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+2 = 2(y+2)$ (2)","G\u1ecdi $x$ l\u00e0 tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi anh hi\u1ec7n nay, $y$ l\u00e0 tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi em hi\u1ec7n nay ($x, y$ nguy\u00ean d\u01b0\u01a1ng)","T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: $\\left\\{ \\begin{align} & x\\text{ }\\text{ }2\\text{ }=3\\left( y-2 \\right) \\\\ & x\\text{ + }2\\text{ }=2\\left( y+2 \\right) \\\\ \\end{align} \\right.$ ","Hai n\u0103m tr\u01b0\u1edbc, tu\u1ed5i anh l\u00e0 $x-2$, tu\u1ed5i em l\u00e0 $y-2$. V\u00ec tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi anh g\u1ea5p ba l\u1ea7n tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi em n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x \u2013 2 =3(y-2)$ (1)"," $\\Leftrightarrow \\left\\{ \\begin{aligned} & x-3y=-4 \\\\ & x-2y=2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=6 \\\\ & x=2y+2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=6 \\\\ & x=14 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)."],"top":70,"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>- G\u1ecdi tu\u1ed5i anh v\u00e0 tu\u1ed5i em hi\u1ec7n nay l\u00e0 \u1ea9n. \u0110\u1eb7t \u0111i\u1ec1u ki\u1ec7n cho \u1ea9n.<br\/>- L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb tu\u1ed5i anh v\u00e0 em hai n\u0103m tr\u01b0\u1edbc<br\/>- L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb tu\u1ed5i em v\u00e0 anh hai n\u0103m sau<br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p c\u1ed9ng \u0111\u1ea1i s\u1ed1<br\/>B\u01b0\u1edbc 3: Ki\u1ec3m tra nghi\u1ec7m v\u00e0 k\u1ebft lu\u1eadn b\u00e0i to\u00e1n<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi $x$ l\u00e0 tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi anh hi\u1ec7n nay, $y$ l\u00e0 tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi em hi\u1ec7n nay ($x, y$ nguy\u00ean d\u01b0\u01a1ng)<br\/>Hai n\u0103m tr\u01b0\u1edbc, tu\u1ed5i anh l\u00e0 $x-2$, tu\u1ed5i em l\u00e0 $y-2$. V\u00ec tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi anh g\u1ea5p ba l\u1ea7n tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi em n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x \u2013 2 =3(y-2)$ (1)<br\/>Hai n\u0103m sau, tu\u1ed5i anh l\u00e0 $x+2$, tu\u1ed5i em l\u00e0 $y+2.$ V\u00ec tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi anh g\u1ea5p hai l\u1ea7n tu\u1ed5i c\u1ee7a ng\u01b0\u1eddi em n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+2 = 2(y+2)$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: $\\left\\{ \\begin{align} & x-2=3\\left( y-2 \\right) \\\\ & x+2=2\\left( y+2 \\right) \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & x-3y=-4 \\\\ & x-2y=2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=6 \\\\ & x=2y+2 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=6 \\\\ & x=14 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n).<br\/><span class='basic_pink'>V\u1eady hi\u1ec7n nay, em $6$ tu\u1ed5i v\u00e0 anh $14$ tu\u1ed5i.<\/span><\/span>"}]}],"id_ques":322},{"time":24,"part":[{"title":"\u0110i\u1ec1n c\u00e1c s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["10"],["36"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"<span class='basic_left'>Trong ph\u00f2ng h\u1ecdc ch\u1ec9 c\u00f3 b\u00e0n gh\u1ebf d\u00e0i. N\u1ebfu x\u1ebfp m\u1ed7i gh\u1ebf $3$ h\u1ecdc sinh th\u00ec $6$ h\u1ecdc sinh kh\u00f4ng c\u00f3 ch\u1ed7 ng\u1ed3i. N\u1ebfu x\u1ebfp m\u1ed7i gh\u1ebf $4$ h\u1ecdc sinh th\u00ec th\u1eeba $1$ gh\u1ebf. H\u1ecfi ph\u00f2ng c\u00f3 bao nhi\u00eau gh\u1ebf, bao nhi\u00eau h\u1ecdc sinh? <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> S\u1ed1 gh\u1ebf ph\u00f2ng c\u00f3 l\u00e0 _input_ v\u00e0 s\u1ed1 h\u1ecdc sinh trong ph\u00f2ng l\u00e0 _input_<\/span>","explain":"<span class='basic_left'> G\u1ecdi $x$ l\u00e0 s\u1ed1 gh\u1ebf v\u00e0 $y$ l\u00e0 s\u1ed1 h\u1ecdc sinh trong ph\u00f2ng. \u0110i\u1ec1u ki\u1ec7n $x, y$ nguy\u00ean d\u01b0\u01a1ng. <br\/> X\u1ebfp m\u1ed7i gh\u1ebf $3$ h\u1ecdc sinh th\u00ec s\u1ed1 h\u1ecdc sinh \u0111\u01b0\u1ee3c ng\u1ed3i gh\u1ebf l\u00e0 $3x$ <br\/> Do c\u00f3 $6$ h\u1ecdc sinh kh\u00f4ng c\u00f3 ch\u1ed7 ng\u1ed3i n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $3x+6=y$ (1)<br\/> X\u1ebfp m\u1ed7i gh\u1ebf 4 h\u1ecdc sinh th\u00ec th\u1eeba m\u1ed9t gh\u1ebf n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $4(x-1)=y$ (2)<br\/> T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& 3x+6=y \\\\ & 4\\left( x-1 \\right)=y \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& 3x+6=y \\\\ & 4x-4=y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x-10=0 \\\\ & y=3x+6 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=10 \\\\ & y=36 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady c\u00f3 $10$ gh\u1ebf v\u00e0 $36$ h\u1ecdc sinh.<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $10$ v\u00e0 $36.$<\/span><\/span>"}]}],"id_ques":323},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>M\u1eabu s\u1ed1 c\u1ee7a m\u1ed9t ph\u00e2n s\u1ed1 l\u1edbn h\u01a1n t\u1eed s\u1ed1 c\u1ee7a n\u00f3 l\u00e0 $3$ \u0111\u01a1n v\u1ecb. N\u1ebfu t\u0103ng c\u1ea3 t\u1eed v\u00e0 m\u1eabu c\u1ee7a n\u00f3 th\u00eam $1$ \u0111\u01a1n v\u1ecb th\u00ec \u0111\u01b0\u1ee3c m\u1ed9t ph\u00e2n s\u1ed1 m\u1edbi b\u1eb1ng $\\dfrac{1}{2}$. T\u00ecm ph\u00e2n s\u1ed1 ban \u0111\u1ea7u.<\/span>","select":["A. $\\dfrac{5}{2}$","B. $\\dfrac{2}{5}$","C. $\\dfrac{4}{5}$"],"hint":"Gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi \u1ea9n l\u00e0 t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 c\u1ee7a ph\u00e2n s\u1ed1 ban \u0111\u1ea7u","explain":"<span class='basic_left'> G\u1ecdi ph\u00e2n s\u1ed1 ban \u0111\u1ea7u l\u00e0 $\\dfrac{a}{b}$ v\u1edbi $a, b \\in \\mathbb {Z}$ v\u00e0 $b \\ne 0$. <br\/>M\u1eabu s\u1ed1 c\u1ee7a ph\u00e2n s\u1ed1 l\u1edbn h\u01a1n t\u1eed s\u1ed1 c\u1ee7a n\u00f3 l\u00e0 $3$ \u0111\u01a1n v\u1ecb n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $b-a=3$(1)<br\/> N\u1ebfu t\u0103ng c\u1ea3 t\u1eed v\u00e0 m\u1eabu th\u00eam $1$ \u0111\u01a1n v\u1ecb, ta \u0111\u01b0\u1ee3c ph\u00e2n s\u1ed1 m\u1edbi l\u00e0 $\\dfrac{a+1}{b+1}; b \\ne -1$ <br\/> V\u00ec ph\u00e2n s\u1ed1 m\u1edbi b\u1eb1ng $\\dfrac{1}{2}$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: <br\/> $\\dfrac{a+1}{b+1}=\\dfrac{1}{2}\\Leftrightarrow \\left( a+1 \\right).2=b+1\\Leftrightarrow 2a-b=-1\\left( 2 \\right)$<br\/>T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: $\\left\\{ \\begin{align} & b-a=3 \\\\ & 2a-b=-1 \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & a=2 \\\\ & b=a+3 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & a=2 \\\\ & b=5 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady ph\u00e2n s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 $\\dfrac{2}{5}$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><br\/><span class='basic_green'>L\u01b0u \u00fd:<\/span><br\/> B\u00e0i to\u00e1n n\u00e0y c\u00f3 th\u1ec3 gi\u1ea3i b\u1eb1ng c\u00e1ch l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh: G\u1ecdi $x$ l\u00e0 t\u1eed s\u1ed1, khi \u0111\u00f3 m\u1eabu s\u1ed1 l\u00e0 $x+3$<\/span>","column":3}]}],"id_ques":324},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'><span class='basic_left'>T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1 bi\u1ebft r\u1eb1ng t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $5$ v\u00e0 t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng hai ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $13.$<br\/><b> C\u00e2u 1: <\/b> G\u1ecdi $x$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c, $y$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb<br\/>Ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb:'' T\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng hai ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $13$ '' l\u00e0: <\/span>","select":["A. $(x+y)^2=13$","B. $x^2+y^2=13^2$","C. $x^2+y^2=13$"],"hint":"Gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi \u1ea9n l\u00e0 t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 c\u1ee7a ph\u00e2n s\u1ed1 ban \u0111\u1ea7u","explain":"<span class='basic_left'> G\u1ecdi $x$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c, $y$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb.<br\/> \u0110i\u1ec1u ki\u1ec7n: $ 0< x \\le 9$; $0 \\le y \\le 9$ v\u00e0 $x,y \\in \\mathbb{N}$ <br\/>V\u00ec t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng hai ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $13$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: ${{x}^{2}}+{{y}^{2}}=13$<br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o hai \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $x^2$ v\u00e0 $13$ <\/span><\/span>","column":3}]}],"id_ques":325},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"<span class='basic_left'>T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1 bi\u1ebft r\u1eb1ng t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $5$ v\u00e0 t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng hai ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $13.$<br\/><b> C\u00e2u 2: <\/b> S\u1ed1 t\u1ef1 nhi\u00ean t\u00ecm \u0111\u01b0\u1ee3c l\u00e0","select":["A.$23$","B. $41$ ","C. $32$ ","D. C\u1ea3 A v\u00e0 C"],"hint":"T\u1eeb gi\u1ea3 thi\u1ebft, l\u1eadp th\u00eam m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh r\u1ed3i k\u1ebft h\u1ee3p v\u1edbi c\u00e2u 1, ta gi\u1ea3i h\u1ec7 \u0111\u1ec3 t\u00ecm hai ch\u1eef s\u1ed1","explain":"<span class='basic_left'> G\u1ecdi $x$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c, $y$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb.<br\/> \u0110i\u1ec1u ki\u1ec7n: $ 0< x \\le 9$; $0 \\le y \\le 9$ v\u00e0 $x,y \\in \\mathbb{N}$<br\/> T\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $5$ n\u00ean $x+y=5$ (1)<br\/>K\u1ebft h\u1ee3p v\u1edbi c\u00e2u 1, ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& x+y=5 \\\\ & {{x}^{2}}+{{y}^{2}}=13 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& x=5-y \\\\ & {{\\left( 5-y \\right)}^{2}}+{{y}^{2}}=13 \\\\ \\end{aligned} \\right.\\Leftrightarrow\\left\\{ \\begin{align}& x=5-y \\\\ & 2{{y}^{2}}-10y+12=0 \\\\ \\end{align} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=5-y \\\\ & {{y}^{2}}-5y+6=0 \\\\ \\end{aligned} \\right.$<br\/> $\\Leftrightarrow \\left\\{ \\begin{aligned} & x=5-y \\\\ & \\left( y-3 \\right)\\left( y-2 \\right)=0 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=5-y \\\\ & \\left[ \\begin{aligned}& y=3 \\\\ & y=2 \\\\ \\end{aligned} \\right. \\\\ \\end{aligned} \\right.$<br\/>V\u1edbi $y=3$ th\u00ec $x=2$ (th\u1ecfa m\u00e3n)<br\/>V\u1edbi $y=2$ th\u00ec $x=3$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $23$ v\u00e0 $32$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span><\/span>","column":2}]}],"id_ques":326},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"<span class='basic_left'>T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1 bi\u1ebft r\u1eb1ng t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $9$ v\u00e0 hi\u1ec7u b\u00ecnh ph\u01b0\u01a1ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $9$ bi\u1ebft ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u1edbn h\u01a1n ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c. ","select":["A. $27$ ","B. $54$","C. $27$","D. $45$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>- G\u1ecdi ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c v\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 \u1ea9n. \u0110\u1eb7t \u0111i\u1ec1u ki\u1ec7n cho \u1ea9n. <br\/>- L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1<br\/>- L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb hi\u1ec7u b\u00ecnh ph\u01b0\u01a1ng c\u00e1c ch\u1eef s\u1ed1<br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh <br\/>B\u01b0\u1edbc 3: Ki\u1ec3m tra nghi\u1ec7m v\u00e0 k\u1ebft lu\u1eadn b\u00e0i to\u00e1n<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi $a$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c, $b$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb. <br\/> \u0110i\u1ec1u ki\u1ec7n: $ 0 < a < b \\le 9$ v\u00e0 $a,b \\in \\mathbb{N}$ <br\/> V\u00ec t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 b\u1eb1ng $9$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $a+b=9$ (1)<br\/> Hi\u1ec7u b\u00ecnh ph\u01b0\u01a1ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $9$ ($b> a$) n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: ${{b}^{2}}-{{a}^{2}}=9$ (2) <br\/> T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& a+b=9 \\\\ & {{b}^{2}}-{{a}^{2}}=9 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& a+b=9 \\\\ & \\left( b-a \\right)\\left( b+a \\right)=9 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& a+b=9 \\\\ & \\left( b-a \\right).9=9 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & a+b=9 \\\\ & b-a=1 \\\\ \\end{aligned} \\right.$<br\/> $\\Leftrightarrow \\left\\{ \\begin{aligned}& 2a=8 \\\\ & b=a+1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & a=4 \\\\ & b=5 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $45$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D.<\/span><\/span>","column":2}]}],"id_ques":327},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1 bi\u1ebft r\u1eb1ng hi\u1ec7u hai l\u1ea7n ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c v\u00e0 $5$ l\u1ea7n ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $1$ v\u00e0 ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c chia cho ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb \u0111\u01b0\u1ee3c th\u01b0\u01a1ng l\u00e0 $2$ v\u00e0 d\u01b0 c\u0169ng l\u00e0 $2$.<br\/><b> C\u00e2u 1: <\/b>G\u1ecdi ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c l\u00e0 $a$ v\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $b$ th\u00ec a, b th\u1ecfa m\u00e3n h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ","select":["A. $\\left\\{ \\begin{align}& 2a=b+2 \\\\ & 2a-5b=1 \\\\ \\end{align} \\right.$ ","B. $\\left\\{ \\begin{align}& a=2b+2 \\\\ & 2a-5b=1\\\\ \\end{align} \\right.$","C. $\\left\\{ \\begin{align}& 2a=b+2 \\\\ & 5a-2b=1 \\\\ \\end{align} \\right.$","D. $\\left\\{ \\begin{align}& a=2b+2 \\\\ & 5a-2b=1\\\\ \\end{align} \\right.$"],"hint":"Chia s\u1ed1 $a$ cho s\u1ed1 $b$ kh\u00e1c $0$ \u0111\u01b0\u1ee3c th\u01b0\u01a1ng $q$ v\u00e0 d\u01b0 l\u00e0 $r$ th\u00ec $a=bq+r$","explain":"<span class='basic_left'>G\u1ecdi $a$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c, $b$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb.<br\/> \u0110i\u1ec1u ki\u1ec7n: $ 0< a \\le 9$; $0 \\le b \\le 9$ v\u00e0 $a,b \\in \\mathbb{N}$<br\/> V\u00ec hi\u1ec7u hai l\u1ea7n ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c v\u00e0 $5$ l\u1ea7n ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $1$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $2a-5b=1$ (1) <br\/> V\u00ec ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c chia cho ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb \u0111\u01b0\u1ee3c th\u01b0\u01a1ng l\u00e0 $2$ v\u00e0 d\u01b0 c\u0169ng l\u00e0 $2$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $a=2b+2$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& a=2b+2 \\\\ & 2a-5b=1 \\\\ \\end{align} \\right.$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/span><\/span>","column":2}]}],"id_ques":328},{"time":24,"part":[{"title":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["83"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"<span class='basic_left'>T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1 bi\u1ebft r\u1eb1ng hi\u1ec7u hai l\u1ea7n ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c v\u00e0 $5$ l\u1ea7n ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $1$ v\u00e0 ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c chia cho ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb \u0111\u01b0\u1ee3c th\u01b0\u01a1ng l\u00e0 $2$ v\u00e0 d\u01b0 c\u0169ng l\u00e0 $2$. <br\/><b> C\u00e2u 2: <\/b>S\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 _input_","hint":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh t\u00ecm \u0111\u01b0\u1ee3c \u1edf c\u00e2u 1","explain":"<span class='basic_left'>G\u1ecdi $a$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c, $b$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb.<br\/> \u0110i\u1ec1u ki\u1ec7n: $ 0< a \\le 9$; $0 \\le b \\le 9$ v\u00e0 $a,b \\in \\mathbb{N}$<br\/>Ta c\u00f3 s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $\\overline{ab}$ <br\/>Theo k\u1ebft qu\u1ea3 c\u00e2u 1, ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& a=2b+2 \\\\ & 2a-5b=1 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned}& a=2b+2 \\\\ & 2\\left( 2b+2 \\right)-5b=1 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & a=2b+2 \\\\ & b=3 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & a=8 \\\\ & b=3 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $83$<br\/><span class='basic_pink'> Do \u0111\u00f3 \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 $83$.<\/span><\/span>."}]}],"id_ques":329},{"time":24,"part":[{"time":3,"title":"<span class='basic_left'>M\u1ed9t m\u1ea3nh v\u01b0\u1eddn h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 chu vi $34m$. N\u1ebfu t\u0103ng chi\u1ec1u d\u00e0i th\u00eam $3m$ v\u00e0 t\u0103ng chi\u1ec1u r\u1ed9ng m\u1ea3nh v\u01b0\u1eddn th\u00eam $2m$ th\u00ec di\u1ec7n t\u00edch t\u0103ng th\u00eam $45 m^2.$ T\u00ednh chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng m\u1ea3nh v\u01b0\u1eddn.<\/span>","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c l\u1eddi gi\u1ea3i \u0111\u00fang","temp":"sequence","correct":[[[2],[7],[1],[4],[6],[5],[3]]],"list":[{"point":5,"image":"img\/1.png","left":["Chu vi m\u1ea3nh v\u01b0\u1eddn l\u00e0 $34$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $2(a+b)=34$ (1)","Suy ra m\u1ea3nh v\u01b0\u1eddn c\u00f3 chi\u1ec1u d\u00e0i l\u00e0 $12 m$, chi\u1ec1u r\u1ed9ng l\u00e0 $5m$<\/ ","G\u1ecdi chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng m\u1ea3nh v\u01b0\u1eddn l\u1ea7n l\u01b0\u1ee3t l\u00e0 $a (m)$ v\u00e0 $b (m).$ \u0110i\u1ec1u ki\u1ec7n $a>b>0$ ","Do di\u1ec7n t\u00edch t\u0103ng th\u00eam $45 m^2$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $(a+3)(b+2)=ab+45$ (2)","Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, ta t\u00ecm \u0111\u01b0\u1ee3c $a=12$ v\u00e0 $b=5$ (th\u1ecfa m\u00e3n)","<span class='basic_left'>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: $\\left\\{ \\begin{align} & 2a+2b=34 \\\\ & \\left( a+3 \\right)\\left( b+2 \\right)=ab+45 \\\\ \\end{align} \\right.$<\/span>","<span class='basic_left'>Di\u1ec7n t\u00edch m\u1ea3nh v\u01b0\u1eddn l\u00e0 $ab (m^2).$T\u0103ng chi\u1ec1u d\u00e0i th\u00eam $3 m$, t\u0103ng chi\u1ec1u r\u1ed9ng th\u00eam $2 m$ th\u00ec di\u1ec7n t\u00edch m\u1ea3nh \u0111\u1ea5t l\u00e0 $(a+3)(b+2)$ $(m^2)$<\/span> "],"top":85,"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span><br\/>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>+ G\u1ecdi chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng l\u00e0 \u1ea9n. \u0110\u1eb7t \u0111i\u1ec1u ki\u1ec7n cho \u1ea9n<br\/>L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb chu vi c\u1ee7a m\u1ea3nh \u0111\u1ea5t.<br\/>+ L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb di\u1ec7n t\u00edch m\u1ea3nh \u0111\u1ea5t t\u1eeb gi\u1ea3 thi\u1ebft th\u1ee9 hai. <br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1eeba l\u1eadp.<br\/>B\u01b0\u1edbc 3: Ki\u1ec3m tra nghi\u1ec7m c\u00f3 th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n kh\u00f4ng v\u00e0 k\u1ebft lu\u1eadn <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng m\u1ea3nh v\u01b0\u1eddn l\u1ea7n l\u01b0\u1ee3t l\u00e0 $a (m)$ v\u00e0 $b (m).$ \u0110i\u1ec1u ki\u1ec7n $a>b>0$<br\/>Chu vi m\u1ea3nh v\u01b0\u1eddn l\u00e0 $34$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $2(a+b)=34$ (1)<br\/>Di\u1ec7n t\u00edch m\u1ea3nh v\u01b0\u1eddn l\u00e0 $ab (m^2)$<br\/>T\u0103ng chi\u1ec1u d\u00e0i th\u00eam $3 m$, t\u0103ng chi\u1ec1u r\u1ed9ng th\u00eam $2 m$ th\u00ec di\u1ec7n t\u00edch m\u1ea3nh \u0111\u1ea5t l\u00e0 $(a+3)(b+2)$ $(m^2)$<br\/>Do di\u1ec7n t\u00edch t\u0103ng th\u00eam $45 m^2$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $(a+3)(b+2)=ab+45$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: $\\left\\{ \\begin{align} & 2a+2b=34 \\\\ & \\left( a+3 \\right)\\left( b+2 \\right)=ab+45 \\\\ \\end{align} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & 2a+2b=34 \\\\ & ab+2a+3b+6=ab+45 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 2a+2b=34 \\\\ & 2a+3b=39 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & b=5 \\\\ & 2a=34-2b \\\\ \\end{aligned} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & b=5 \\\\ & 2a=24 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & b=5 \\\\ & a=12 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady m\u1ea3nh v\u01b0\u1eddn c\u00f3 chi\u1ec1u d\u00e0i l\u00e0 $12$ $m$, chi\u1ec1u r\u1ed9ng l\u00e0 $5$ $m$<\/span>"}]}],"id_ques":330},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'>M\u1ed9t \u00f4 t\u00f4 \u0111i t\u1eeb t\u1ec9nh $A$ \u0111\u1ebfn t\u1ec9nh $B$ v\u1edbi m\u1ed9t v\u1eadn t\u1ed1c \u0111\u00e3 \u0111\u1ecbnh. N\u1ebfu t\u0103ng v\u1eadn t\u1ed1c th\u00eam $10km\/h$ th\u00ec \u0111\u1ebfn n\u01a1i s\u1edbm h\u01a1n d\u1ef1 \u0111\u1ecbnh $3$ gi\u1edd. N\u1ebfu v\u1eadn t\u1ed1c gi\u1ea3m b\u1edbt $10km\/h$ th\u00ec \u0111\u1ebfn n\u01a1i ch\u1eadm m\u1ea5t $5$ gi\u1edd. <br\/><b> C\u00e2u 1: <\/b>G\u1ecdi v\u1eadn t\u1ed1c v\u00e0 th\u1eddi gian d\u1ef1 \u0111\u1ecbnh c\u1ee7a \u00f4 t\u00f4 l\u1ea7n l\u01b0\u1ee3t l\u00e0 $x$ v\u00e0 $y$ th\u00ec h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh l\u1eadp \u0111\u01b0\u1ee3c l\u00e0:<\/span>","select":["A. $\\left\\{ \\begin{align} & \\left( x-10 \\right)\\left( y+3 \\right)=xy \\\\ & \\left( x+10 \\right)\\left( y-5 \\right)=xy \\\\ \\end{align} \\right.$","B. $\\left\\{ \\begin{align} & \\left( x+10 \\right)\\left( y+3 \\right)=xy \\\\ & \\left( x-10 \\right)\\left( y-5 \\right)=xy \\\\ \\end{align} \\right.$","C. $\\left\\{ \\begin{align} & \\left( x+10 \\right)\\left( y-3 \\right)=xy \\\\ & \\left( x-10 \\right)\\left( y+5 \\right)=xy \\\\ \\end{align} \\right.$","D. $\\left\\{ \\begin{align} & \\left( x-10 \\right)\\left( y-3 \\right)=xy \\\\ & \\left( x+10 \\right)\\left( y+5 \\right)=xy \\\\ \\end{align} \\right.$"],"hint":"","explain":"<span class='basic_left'>G\u1ecdi v\u1eadn t\u1ed1c d\u1ef1 \u0111\u1ecbnh c\u1ee7a \u00f4 t\u00f4 l\u00e0 $x\\, (km\/h)$, $x>10;$ th\u1eddi gian d\u1ef1 \u0111\u1ecbnh c\u1ee7a \u00f4 t\u00f4 l\u00e0 $y \\,(h),$ $y>3.$<br\/> Khi \u0111\u00f3 \u0111\u1ed9 d\u00e0i qu\u00e3ng \u0111\u01b0\u1eddng $AB$ l\u00e0 $xy$ $(km)$.<br\/>N\u1ebfu v\u1eadn t\u1ed1c t\u0103ng th\u00eam $10 km\/h,$ t\u1ee9c xe \u0111i v\u1edbi v\u1eadn t\u1ed1c $x+10$ $(km\/h)$ th\u00ec th\u1eddi gian \u0111i \u0111\u01b0\u1ee3c l\u00e0 $y-3 (h)$ <br\/> Suy ra \u0111\u1ed9 d\u00e0i qu\u00e3ng \u0111\u01b0\u1eddng $AB$ l\u00e0 $\\left( x+10 \\right)\\left( y-3 \\right)$ (km) <br\/> Do qu\u00e3ng \u0111\u01b0\u1eddng $AB$ kh\u00f4ng \u0111\u1ed5i n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: <\/span><br\/> $\\left( x+10 \\right)\\left( y-3 \\right)=xy$(1)<br\/><span class='basic_left'>T\u01b0\u01a1ng t\u1ef1, n\u1ebfu v\u1eadn t\u1ed1c gi\u1ea3m b\u1edbt $10$ $km\/h$ th\u00ec \u0111\u1ebfn n\u01a1i ch\u1eadm m\u1ea5t $5$ gi\u1edd, ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<\/span><br\/>$\\left( x-10 \\right)\\left( y+5 \\right)=xy$ (2)<br\/><span class='basic_left'>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: $\\left\\{ \\begin{align} & \\left( x+10 \\right)\\left( y-3 \\right)=xy \\\\ & \\left( x-10 \\right)\\left( y+5 \\right)=xy \\\\ \\end{align} \\right.$ <br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C.<\/span><\/span>","column":2}]}],"id_ques":331},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>M\u1ed9t \u00f4 t\u00f4 \u0111i t\u1eeb t\u1ec9nh $A$ \u0111\u1ebfn t\u1ec9nh $B$ v\u1edbi m\u1ed9t v\u1eadn t\u1ed1c \u0111\u00e3 \u0111\u1ecbnh. N\u1ebfu t\u0103ng v\u1eadn t\u1ed1c th\u00eam $10km\/h$ th\u00ec \u0111\u1ebfn n\u01a1i s\u1edbm h\u01a1n d\u1ef1 \u0111\u1ecbnh $3$ gi\u1edd. N\u1ebfu v\u1eadn t\u1ed1c gi\u1ea3m b\u1edbt $10km\/h$ th\u00ec \u0111\u1ebfn n\u01a1i ch\u1eadm m\u1ea5t $5$ gi\u1edd. <br\/><b> C\u00e2u 2: <\/b>\u0110\u1ed9 d\u00e0i qu\u00e3ng \u0111\u01b0\u1eddng $AB$ l\u00e0<\/span>","select":["A. $450$ $km$ ","B. $600$ $km$","C. $500$ $km$"],"hint":"Qu\u00e3ng \u0111\u01b0\u1eddng $=$ V\u1eadn t\u1ed1c . Th\u1eddi gian","explain":"<span class='basic_left'>G\u1ecdi v\u1eadn t\u1ed1c d\u1ef1 \u0111\u1ecbnh c\u1ee7a \u00f4 t\u00f4 l\u00e0 $x\\, (km\/h)$, $x>10;$ th\u1eddi gian d\u1ef1 \u0111\u1ecbnh c\u1ee7a \u00f4 t\u00f4 l\u00e0 $y \\,(h),$ $y>3.$<br\/>Theo c\u00e2u 1, ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh (I) $\\left\\{ \\begin{align} & \\left( x+10 \\right)\\left( y-3 \\right)=xy \\\\ & \\left( x-10 \\right)\\left( y+5 \\right)=xy \\\\ \\end{align} \\right.$ <br\/>Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\left( I \\right)\\Leftrightarrow \\left\\{ \\begin{aligned} & xy-3x+10y-30=xy \\\\ & xy+5x-10y-50=xy \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & -3x+10y=30 \\\\ & 5x-10y=50 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 2x=80 \\\\ & x-2y=10 \\\\ \\end{aligned} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & x=40 \\\\ & 2y=x-10 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=40 \\\\ & 2y=30 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=40 \\\\ & y=15 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>Suy ra, \u0111\u1ed9 d\u00e0i qu\u00e3ng \u0111\u01b0\u1eddng $AB$ l\u00e0 $x.y=40.15=600$ $(km)$<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":3}]}],"id_ques":332},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'> \u0110o\u1ea1n \u0111\u01b0\u1eddng $AB$ d\u00e0i $200 km$. C\u00f9ng l\u00fac m\u1ed9t xe m\u00e1y \u0111i t\u1eeb $A$ v\u00e0 m\u1ed9t \u00f4 t\u00f4 \u0111i t\u1eeb $B,$ xe m\u00e1y v\u00e0 \u00f4 t\u00f4 g\u1eb7p nhau t\u1ea1i $C$ c\u00e1ch $A$ $80 km.$ N\u1ebfu \u00f4 t\u00f4 kh\u1edfi h\u00e0nh sau xe m\u00e1y $1$ gi\u1edd th\u00ec g\u1eb7p nhau t\u1ea1i $D$ c\u00e1ch $C$ $24 km.$ <br\/><b> C\u00e2u 1: <\/b> G\u1ecdi v\u1eadn t\u1ed1c xe m\u00e1y l\u00e0 $x (km\/h)$ v\u00e0 v\u1eadn t\u1ed1c \u00f4 t\u00f4 l\u00e0 $y(km\/h)$ th\u00ec ta l\u1eadp \u0111\u01b0\u1ee3c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0<\/span>","select":["A. $\\left\\{ \\begin{align}& \\dfrac{3}{x}=\\dfrac{2}{y} \\\\ & \\dfrac{104}{x}=\\dfrac{96}{y}+1 \\\\ \\end{align} \\right.$ ","B. $\\left\\{ \\begin{align}& \\dfrac{2}{x}=\\dfrac{3}{y} \\\\ & \\dfrac{96}{x}=\\dfrac{104}{y}+1 \\\\ \\end{align} \\right.$ ","C. $\\left\\{ \\begin{align}& \\dfrac{2}{x}=\\dfrac{3}{y} \\\\ & \\dfrac{104}{x}=\\dfrac{96}{y}+1 \\\\ \\end{align} \\right.$ "],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<\/span><br\/>Chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a hai xe \u0111\u01b0\u1ee3c m\u00f4 t\u1ea3 b\u1eb1ng h\u00ecnh v\u1ebd sau:<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai16/lv2/img\/D3.1.png' \/><\/center><br\/>- Khi hai xe \u0111i c\u00f9ng l\u00fac th\u00ec \u0111o\u1ea1n \u0111\u01b0\u1eddng xe m\u00e1y \u0111i l\u00e0 $AC,$ \u00f4 t\u00f4 l\u00e0 $BC$<br\/>- N\u1ebfu xe m\u00e1y kh\u1edfi h\u00e0nh sau \u00f4 t\u00f4 $1$ gi\u1edd th\u00ec \u0111o\u1ea1n \u0111\u01b0\u1eddng xe m\u00e1y \u0111i l\u00e0 $AD$ v\u00e0 \u00f4 t\u00f4 l\u00e0 $BD.$<br\/><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/>L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>+ G\u1ecdi \u1ea9n l\u00e0 v\u1eadn t\u1ed1c c\u1ee7a xe m\u00e1y v\u00e0 \u00f4 t\u00f4. <br\/>+ X\u00e1c \u0111\u1ecbnh qu\u00e3ng \u0111\u01b0\u1eddng m\u00e0 t\u1eebng xe \u0111\u00e3 \u0111i khi hai xe \u0111i c\u00f9ng l\u00fac r\u1ed3i l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb th\u1eddi gian<br\/> + X\u00e1c \u0111\u1ecbnh qu\u00e3ng \u0111\u01b0\u1eddng m\u00e0 t\u1eebng xe \u0111\u00e3 \u0111i khi \u00f4 t\u00f4 xu\u1ea5t ph\u00e1t sau $1$ gi\u1edd r\u1ed3i l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb th\u1eddi gian c\u1ee7a hai xe<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a xe m\u00e1y l\u00e0 $x\\, (km\/h)$ v\u00e0 v\u1eadn t\u1ed1c \u00f4 t\u00f4 l\u00e0 $y\\, (km\/h).$ \u0110i\u1ec1u ki\u1ec7n $x,y$ d\u01b0\u01a1ng <br\/> Khi hai xe xu\u1ea5t ph\u00e1t c\u00f9ng l\u00fac, xe m\u00e1y v\u00e0 \u00f4 t\u00f4 g\u1eb7p nhau t\u1ea1i $C$ c\u00e1ch $A$ $80 km$ n\u00ean qu\u00e3ng \u0111\u01b0\u1eddng xe m\u00e1y \u0111i l\u00e0 $80km,$ \u00f4 t\u00f4 l\u00e0 $120 km.$ Khi \u0111\u00f3 do hai xe c\u00f9ng \u0111i h\u1ebft th\u1eddi gian nh\u01b0 nhau n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: ph\u01b0\u01a1ng tr\u00ecnh:<\/span> <br\/> $\\dfrac{80}{x}=\\dfrac{120}{y}$ hay $\\dfrac{2}{x}=\\dfrac{3}{y}$(1) <br\/> <span class='basic_left'> N\u1ebfu \u00f4 t\u00f4 kh\u1edfi h\u00e0nh sau xe m\u00e1y $1$ gi\u1edd th\u00ec g\u1eb7p nhau t\u1ea1i $D$ c\u00e1ch $C$ $24 km$ th\u00ec xe m\u00e1y \u0111i \u0111\u01b0\u1ee3c qu\u00e3ng \u0111\u01b0\u1eddng l\u00e0 $80+24=104 (km)$ v\u00e0 \u00f4 t\u00f4 \u0111i \u0111\u01b0\u1ee3c qu\u00e3ng \u0111\u01b0\u1eddng l\u00e0 $120-24=96 (km).$ Khi \u0111\u00f3 ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<\/span><br\/> $\\dfrac{104}{x}=\\dfrac{96}{y}+1$ (2)<br\/><span class='basic_left'>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<\/span><br\/>$\\left\\{ \\begin{align} & \\dfrac{2}{x}=\\dfrac{3}{y} \\\\ & \\dfrac{104}{x}=\\dfrac{96}{y}+1 \\\\ \\end{align} \\right.$ <br\/><span class='basic_left'><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":3}]}],"id_ques":333},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["40"],["60"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>\u0110o\u1ea1n \u0111\u01b0\u1eddng $AB$ d\u00e0i $200 km$. C\u00f9ng l\u00fac m\u1ed9t xe m\u00e1y \u0111i t\u1eeb $A$ v\u00e0 m\u1ed9t \u00f4 t\u00f4 \u0111i t\u1eeb $B,$ xe m\u00e1y v\u00e0 \u00f4 t\u00f4 g\u1eb7p nhau t\u1ea1i $C$ c\u00e1ch $A$ $80 km.$ N\u1ebfu \u00f4 t\u00f4 kh\u1edfi h\u00e0nh sau xe m\u00e1y $1$ gi\u1edd th\u00ec g\u1eb7p nhau t\u1ea1i $D$ c\u00e1ch $C$ $24 km.$ <br\/><b> C\u00e2u 2: <\/b> V\u1eadn t\u1ed1c c\u1ee7a xe m\u00e1y l\u00e0 _input_ $(km\/h)$v\u00e0 v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 l\u00e0 _input_ $(km\/h)$<\/span>","hint":"Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh thu \u0111\u01b0\u1ee3c \u1edf c\u00e2u 1 b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1eb7t \u1ea9n ph\u1ee5","explain":"<span class='basic_left'>G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a xe m\u00e1y l\u00e0 $x (km\/h)$ v\u00e0 v\u1eadn t\u1ed1c \u00f4 t\u00f4 l\u00e0 $y (km\/h).$ \u0110i\u1ec1u ki\u1ec7n$x,y$ d\u01b0\u01a1ng <br\/> Theo k\u1ebft qu\u1ea3 <b>c\u00e2u 1<\/b>, ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align}& \\dfrac{2}{x}=\\dfrac{3}{y} \\\\ & \\dfrac{104}{x}=\\dfrac{96}{y}+1 \\\\ \\end{align} \\right.$ <br\/>\u0110\u1eb7t $u=\\dfrac{1}{x},v=\\dfrac{1}{y},$ h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tr\u1edf th\u00e0nh <br\/>$\\left\\{ \\begin{align} & 2u=3v \\\\ & 104u-96v=1 \\\\ \\end{align} \\right.$ <br\/>Gi\u1ea3i h\u1ec7 n\u00e0y ta \u0111\u01b0\u1ee3c $\\left\\{ \\begin{aligned} & u=\\dfrac{1}{40} \\\\ & v=\\dfrac{1}{60} \\\\ \\end{aligned} \\right.$ <br\/>Suy ra $\\left\\{ \\begin{aligned} & \\dfrac{1}{x}=\\dfrac{1}{40} \\\\ & \\dfrac{1}{y}=\\dfrac{1}{60} \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=40 \\\\ & y=60 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady v\u1eadn t\u1ed1c c\u1ee7a xe m\u00e1y l\u00e0 $40 km\/h,$ c\u1ee7a \u00f4 t\u00f4 l\u00e0 $60km\/h$<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $40;60$<\/span><\/span>"}]}],"id_ques":334},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>M\u1ed9t ca n\u00f4 xu\u00f4i d\u00f2ng m\u1ed9t qu\u00e3ng s\u00f4ng d\u00e0i $80$ $km$ v\u00e0 sau \u0111\u00f3 ng\u01b0\u1ee3c d\u00f2ng h\u1ebft $8$ gi\u1edd $20$ ph\u00fat. N\u1ebfu c\u00f9ng tr\u00ean qu\u00e3ng s\u00f4ng \u1ea5y, ca n\u00f4 xu\u00f4i d\u00f2ng $24$ $km$ v\u00e0 ng\u01b0\u1ee3c d\u00f2ng $32$ $km$ th\u00ec h\u1ebft $3$ gi\u1edd. <br\/><b> C\u00e2u 1: <\/b>G\u1ecdi v\u1eadn t\u1ed1c ca n\u00f4 l\u00e0 $x$ $(km\/h),$ v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc l\u00e0 $y$ $(km\/h)$ th\u00ec ta l\u1eadp \u0111\u01b0\u1ee3c h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0<\/span>","select":["A. $\\left\\{ \\begin{align} & \\dfrac{80}{x+y}+\\dfrac{80}{x-y}=\\dfrac{25}{3} \\\\ & \\dfrac{32}{x+y}+\\dfrac{24}{x-y}=3 \\\\ \\end{align} \\right.$ ","B. $\\left\\{ \\begin{align} & \\dfrac{80}{x+y}+\\dfrac{80}{x-y}=\\dfrac{25}{3} \\\\ & \\dfrac{24}{x+y}+\\dfrac{32}{x-y}=3 \\\\ \\end{align} \\right.$","C. $\\left\\{ \\begin{align} & \\dfrac{80}{x+y}+\\dfrac{80}{y-x}=\\dfrac{25}{3} \\\\ & \\dfrac{24}{x+y}+\\dfrac{32}{y-x}=3 \\\\ \\end{align} \\right.$","D. $\\left\\{ \\begin{align} & \\dfrac{80}{x+y}+\\dfrac{80}{y-x}=3 \\\\ & \\dfrac{24}{x+y}+\\dfrac{32}{y-x}=\\dfrac{25}{3} \\\\ \\end{align} \\right.$"],"hint":" V\u1eadn t\u1ed1c xu\u00f4i d\u00f2ng $=$ v\u1eadn t\u1ed1c th\u1ef1c $+$ v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc; <br\/> V\u1eadn t\u1ed1c ng\u01b0\u1ee3c d\u00f2ng $=$ v\u1eadn t\u1ed1c th\u1ef1c $-$ v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/>L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh<br\/>+ G\u1ecdi \u1ea9n l\u00e0 v\u1eadn t\u1ed1c th\u1ef1c c\u1ee7a ca n\u00f4 v\u00e0 v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc. X\u00e1c \u0111\u1ecbnh v\u1eadn t\u1ed1c c\u1ee7a ca n\u00f4 khi xu\u00f4i d\u00f2ng v\u00e0 ng\u01b0\u1ee3c d\u00f2ng<br\/>+ L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb th\u1eddi gian c\u1ee7a ca n\u00f4 v\u1edbi t\u1eebng gi\u1ea3 thi\u1ebft b\u00e0i to\u00e1n<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi v\u1eadn t\u1ed1c ca n\u00f4 l\u00e0 $x$ $(km\/h),$ v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc l\u00e0 $y$ $(km\/h)$. \u0110i\u1ec1u ki\u1ec7n: $x>y>0 $<br\/>V\u1eadn t\u1ed1c xu\u00f4i d\u00f2ng c\u1ee7a ca n\u00f4 l\u00e0 $x+y$ $(km\/h);$ v\u1eadn t\u1ed1c ng\u01b0\u1ee3c d\u00f2ng c\u1ee7a ca n\u00f4 l\u00e0 $x-y$ $(km\/h)$<br\/>Ca n\u00f4 xu\u00f4i d\u00f2ng qu\u00e3ng s\u00f4ng d\u00e0i $80$ $km$ h\u1ebft $\\dfrac{80}{x+y}$ $(h)$ v\u00e0 sau \u0111\u00f3 ng\u01b0\u1ee3c d\u00f2ng $80km$ h\u1ebft $\\dfrac{80}{x-y}$ $(h).$ V\u00ec t\u1ed5ng th\u1eddi gian h\u1ebft $8$ gi\u1edd $20$ ph\u00fat $=\\dfrac{25}{3}$ gi\u1edd n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: <\/span><br\/> $\\dfrac{80}{x+y}+\\dfrac{80}{x-y}=\\dfrac{25}{3}$ (1)<br\/><span class='basic_left'>Ca n\u00f4 xu\u00f4i d\u00f2ng $24$ $km$ h\u1ebft $\\dfrac{24}{x+y}$ $(h)$ v\u00e0 sau \u0111\u00f3 ng\u01b0\u1ee3c d\u00f2ng $32$ $km$ h\u1ebft $\\dfrac{32}{x-y}$ (h). V\u00ec t\u1ed5ng th\u1eddi gian h\u1ebft $3$ gi\u1edd n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<\/span> $\\dfrac{24}{x+y}+\\dfrac{32}{x-y}=3$(2)<br\/><span class='basic_left'>T\u1eeb (1) v\u00e0 (2) ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<\/span>$\\left\\{ \\begin{align} & \\dfrac{80}{x+y}+\\dfrac{80}{x-y}=\\dfrac{25}{3} \\\\ & \\dfrac{24}{x+y}+\\dfrac{32}{x-y}=3 \\\\ \\end{align} \\right.$<br\/><span class='basic_left'><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":2}]}],"id_ques":335},{"time":24,"part":[{"title":"\u0110i\u1ec1n t\u1eeb th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["20"],["4"]]],"list":[{"point":5,"width":150,"content":"","type_input":"","ques":"<span class='basic_left'>M\u1ed9t ca n\u00f4 xu\u00f4i d\u00f2ng m\u1ed9t qu\u00e3ng s\u00f4ng d\u00e0i $80$ $km$ v\u00e0 sau \u0111\u00f3 ng\u01b0\u1ee3c d\u00f2ng h\u1ebft $8$ gi\u1edd $20$ ph\u00fat. N\u1ebfu c\u00f9ng tr\u00ean qu\u00e3ng s\u00f4ng \u1ea5y, ca n\u00f4 xu\u00f4i d\u00f2ng $24$ $km$ v\u00e0 ng\u01b0\u1ee3c d\u00f2ng $32$ $km$ th\u00ec h\u1ebft $3$ gi\u1edd. <br\/><b> C\u00e2u 2:<\/b> T\u00ednh v\u1eadn t\u1ed1c th\u1ef1c c\u1ee7a ca n\u00f4 v\u00e0 v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc.<br\/><b>\u0110\u00e1p s\u1ed1: <\/b>V\u1eadn t\u1ed1c th\u1ef1c c\u1ee7a ca n\u00f4 l\u00e0 _input_$km\/h$ v\u00e0 v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc l\u00e0 _input_$km\/h$<\/span> ","hint":"","explain":"<span class='basic_left'>G\u1ecdi v\u1eadn t\u1ed1c ca n\u00f4 l\u00e0 $x$ $(km\/h),$ v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc l\u00e0 $y$ $(km\/h)$. \u0110i\u1ec1u ki\u1ec7n: $x>y>0 $<br\/>Theo c\u00e2u 1, ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{align} & \\dfrac{80}{x+y}+\\dfrac{80}{x-y}=\\dfrac{25}{3} \\\\ & \\dfrac{24}{x+y}+\\dfrac{32}{x-y}=3 \\\\ \\end{align} \\right.$<br\/>\u0110\u1eb7t $\\dfrac{1}{x+y}=u;\\dfrac{1}{x-y}=v$.<br\/> Ta c\u00f3 $\\left\\{ \\begin{align} & 80u+80v=\\dfrac{25}{3} \\\\ & 24u+32v=3 \\\\ \\end{align} \\right.$ <br\/>Gi\u1ea3i h\u1ec7 ta t\u00ecm \u0111\u01b0\u1ee3c $u=\\dfrac{1}{24};v=\\dfrac{1}{16}$ <br\/>Suy ra $\\left\\{ \\begin{aligned} & x+y=24 \\\\ & x-y=16 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & 2x=40 \\\\ & y=x-16 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=20 \\\\ & y=4 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady v\u1eadn t\u1ed1c th\u1ef1c c\u1ee7a ca n\u00f4 l\u00e0 $20km\/h$ v\u00e0 v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc l\u00e0 $4km\/h$<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 l\u00e0 $20$; $4.$<\/span><\/span>"}]}],"id_ques":336},{"time":24,"part":[{"time":3,"title":"Hai xe t\u1ea3i ph\u1ea3i ch\u1edf h\u1ebft m\u1ed9t s\u1ed1 h\u00e0ng trong $6$ gi\u1edd. N\u1ebfu sau khi xe th\u1ee9 nh\u1ea5t \u0111\u00e3 ch\u1edf \u0111\u01b0\u1ee3c $\\dfrac{3}{5}$ s\u1ed1 h\u00e0ng v\u00e0 xe th\u1ee9 hai tr\u1edf n\u1ed1t s\u1ed1 h\u00e0ng c\u00f2n l\u1ea1i th\u00ec ph\u1ea3i m\u1ea5t $6$ gi\u1edd xe th\u1ee9 hai m\u1edbi ch\u1edf h\u1ebft s\u1ed1 h\u00e0ng tr\u00ean. H\u1ecfi n\u1ebfu m\u1ed7i xe ch\u1edf m\u1ed9t m\u00ecnh th\u00ec bao l\u00e2u m\u1edbi tr\u1edf h\u1ebft s\u1ed1 h\u00e0ng?","title_trans":"S\u1eafp x\u1ebfp c\u00e1c c\u00e2u \u0111\u1ec3 \u0111\u01b0\u1ee3c l\u1eddi gi\u1ea3i \u0111\u00fang","temp":"sequence","correct":[[[3],[7],[1],[6],[5],[2],[4]]],"list":[{"point":5,"image":"img\/1.png","left":["Trong $1$ gi\u1edd, hai xe ch\u1edf \u0111\u01b0\u1ee3c $\\dfrac{1}{6}$ s\u1ed1 h\u00e0ng n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: ph\u01b0\u01a1ng tr\u00ecnh $\\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{6}$ (1) ","V\u1eady xe th\u1ee9 nh\u1ea5t ch\u1edf m\u1ed9t m\u00ecnh h\u1ebft h\u00e0ng trong $10$ gi\u1edd, xe th\u1ee9 hai tr\u1edf m\u1ed9t m\u00ecnh h\u1ebft h\u00e0ng trong $15$ gi\u1edd. ","G\u1ecdi $x$ gi\u1edd l\u00e0 th\u1eddi gian xe t\u1ea3i I ch\u1edf m\u1ed9t m\u00ecnh h\u1ebft h\u00e0ng; $y$ gi\u1edd l\u00e0 th\u1eddi gian xe t\u1ea3i II ch\u1edf m\u1ed9t m\u00ecnh h\u1ebft h\u00e0ng. \u0110i\u1ec1u ki\u1ec7n $x>0,y>0$ ","Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh, ta t\u00ecm \u0111\u01b0\u1ee3c $x=10$ v\u00e0 $y=15$ (th\u1ecfa m\u00e3n)","T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:$\\left\\{ \\begin{align} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{6} \\\\ & \\dfrac{6}{y}=\\dfrac{2}{5} \\\\ \\end{align} \\right.$","Trong $1$ gi\u1edd xe t\u1ea3i I ch\u1edf \u0111\u01b0\u1ee3c $\\dfrac{1}{x}$ s\u1ed1 h\u00e0ng, xe t\u1ea3i II ch\u1edf \u0111\u01b0\u1ee3c $\\dfrac{1}{y}$ s\u1ed1 h\u00e0ng","Xe th\u1ee9 nh\u1ea5t ch\u1edf \u0111\u01b0\u1ee3c $\\dfrac{3}{5}$ s\u1ed1 h\u00e0ng th\u00ec s\u1ed1 h\u00e0ng c\u00f2n l\u1ea1i l\u00e0 $1-\\dfrac{3}{5}=\\dfrac{2}{5}$m\u00e0 xe II ch\u1edf n\u1ed1t s\u1ed1 h\u00e0ng \u0111\u00f3 trong $6$ gi\u1edd n\u00ean $\\dfrac{6}{y}=\\dfrac{2}{5}$ (2) "],"top":105,"hint":"G\u1ecdi \u1ea9n l\u00e0 th\u1eddi gian m\u1ed7i xe ch\u1edf m\u1ed9t m\u00ecnh h\u1ebft h\u00e0ng. T\u1eeb gi\u1ea3 thi\u1ebft b\u00e0i to\u00e1n, ta l\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh hai \u1ea9n<br\/>Ch\u00fa \u00fd: S\u1ed1 ph\u1ea7n c\u00f4ng vi\u1ec7c m\u00e0 m\u1ed7i xe ph\u1ea3i ch\u1edf trong m\u1ed9t gi\u1edd v\u00e0 th\u1eddi gian c\u1ea7n thi\u1ebft \u0111\u1ec3 m\u1ed7i xe ch\u1edf h\u1ebft h\u00e0ng l\u00e0 hai \u0111\u1ea1i l\u01b0\u1ee3ng t\u1ec9 l\u1ec7 ngh\u1ecbch","explain":"<span class='basic_left'>G\u1ecdi $x$ gi\u1edd l\u00e0 th\u1eddi gian xe t\u1ea3i I ch\u1edf m\u1ed9t m\u00ecnh h\u1ebft h\u00e0ng; $y$ gi\u1edd l\u00e0 th\u1eddi gian xe t\u1ea3i II ch\u1edf m\u1ed9t m\u00ecnh h\u1ebft h\u00e0ng. \u0110i\u1ec1u ki\u1ec7n $x>0,y>0$<br\/>Trong $1$ gi\u1edd xe t\u1ea3i I ch\u1edf \u0111\u01b0\u1ee3c $\\dfrac{1}{x}$ s\u1ed1 h\u00e0ng, xe t\u1ea3i II ch\u1edf \u0111\u01b0\u1ee3c $\\dfrac{1}{y}$ s\u1ed1 h\u00e0ng<br\/>Trong $1$ gi\u1edd, hai xe ch\u1edf \u0111\u01b0\u1ee3c $\\dfrac{1}{6}$ s\u1ed1 h\u00e0ng n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: ph\u01b0\u01a1ng tr\u00ecnh $\\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{6}$ (1)<br\/>Xe th\u1ee9 nh\u1ea5t ch\u1edf \u0111\u01b0\u1ee3c $\\dfrac{3}{5}$ s\u1ed1 h\u00e0ng th\u00ec s\u1ed1 h\u00e0ng c\u00f2n l\u1ea1i l\u00e0 $1-\\dfrac{3}{5}=\\dfrac{2}{5}$m\u00e0 xe II ch\u1edf n\u1ed1t s\u1ed1 h\u00e0ng \u0111\u00f3 trong $6$ gi\u1edd n\u00ean $\\dfrac{6}{y}=\\dfrac{2}{5}$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:$\\left\\{ \\begin{align} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{6} \\\\ & \\dfrac{6}{y}=\\dfrac{2}{5} \\\\ \\end{align} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{6} \\\\ & y=15 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & \\dfrac{1}{x}+\\dfrac{1}{15}=\\dfrac{1}{6} \\\\ & y=15 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=10 \\\\ & y=15 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n)<br\/>V\u1eady xe th\u1ee9 nh\u1ea5t ch\u1edf m\u1ed9t m\u00ecnh h\u1ebft h\u00e0ng trong $10$ gi\u1edd, xe th\u1ee9 hai tr\u1edf m\u1ed9t m\u00ecnh h\u1ebft h\u00e0ng trong $15$ gi\u1edd.<\/span>"}]}],"id_ques":337},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["28"],["21"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>Hai v\u00f2i n\u01b0\u1edbc c\u00f9ng ch\u1ea3y v\u00e0o m\u1ed9t b\u1ec3 n\u01b0\u1edbc c\u1ea1n th\u00ec sau $12$ gi\u1edd b\u1ec3 \u0111\u1ea7y. N\u1ebfu hai v\u00f2i c\u00f9ng ch\u1ea3y trong $8$ gi\u1edd th\u00ec kh\u00f3a v\u00f2i I, v\u00f2i II ti\u1ebfp t\u1ee5c ch\u1ea3y v\u1edbi n\u0103ng su\u1ea5t g\u1ea5p \u0111\u00f4i th\u00ec sau \u0111\u00f3 $3$ gi\u1edd $30$ ph\u00fat n\u1eefa m\u1edbi \u0111\u1ea7y b\u1ec3. H\u1ecfi n\u1ebfu m\u1ed7i v\u00f2i ch\u1ea3y ri\u00eang v\u1edbi n\u0103ng su\u1ea5t b\u00ecnh th\u01b0\u1eddng th\u00ec sau bao l\u00e2u m\u1edbi \u0111\u1ea7y b\u1ec3? <br\/><b> \u0110\u00e1p s\u1ed1: <\/b>Th\u1eddi gian v\u00f2i I ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3 l\u00e0 _input_gi\u1edd<br\/> Th\u1eddi gian v\u00f2i II ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3 l\u00e0 _input_gi\u1edd<\/span>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span><br\/>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>+ G\u1ecdi \u1ea9n l\u00e0 th\u1eddi gian m\u1ed7i v\u00f2i ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3.<br\/>+ T\u1eeb gi\u1ea3i thi\u1ebft hai v\u00f2i c\u00f9ng ch\u1ea3y th\u00ec sau 12 gi\u1edd \u0111\u1ea7y b\u1ec3, ta thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb trong 1 gi\u1edd, s\u1ed1 ph\u1ea7n b\u1ec3 hai v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c<br\/>+T\u1eeb gi\u1ea3 thi\u1ebft th\u1ee9 hai, ta t\u00ednh xem t\u1eeb l\u00fac v\u00f2i hai ch\u1ea3y m\u1ed9t m\u00ecnh th\u00ec v\u00f2i II ch\u1ea3y \u0111\u01b0\u1ee3c bao nhi\u00eau ph\u1ea7n b\u1ec3 r\u1ed3i t\u1eeb \u0111\u00f3 thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh. <br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1eeba l\u1eadp.<br\/>B\u01b0\u1edbc 3: Ki\u1ec3m tra nghi\u1ec7m c\u00f3 th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n kh\u00f4ng v\u00e0 k\u1ebft lu\u1eadn b\u00e0i to\u00e1n <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> \u0110\u1ed5i: 3 gi\u1edd 30 ph\u00fat $=\\dfrac{7}{2}$ gi\u1edd <br\/> G\u1ecdi $x$ gi\u1edd l\u00e0 th\u1eddi gian v\u00f2i I ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3; $y$ gi\u1edd l\u00e0 th\u1eddi gian v\u00f2i II ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3.<br\/> \u0110i\u1ec1u ki\u1ec7n $ x>0,y>0$<br\/>Trong $1$ gi\u1edd v\u00f2i I ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{1}{x}$ b\u1ec3, v\u00f2i II ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{1}{y}$ b\u1ec3<br\/>Trong $1$ gi\u1edd, hai v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{1}{12}$ b\u1ec3 n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{12}$ (1)<br\/>Hai v\u00f2i ch\u1ea3y trong $8$ gi\u1edd th\u00ec \u0111\u01b0\u1ee3c $\\dfrac{8}{12}=\\dfrac{2}{3}$ b\u1ec3.<br\/> Sau \u0111\u00f3 kh\u00f3a v\u00f2i I v\u00e0 v\u00f2i II ch\u1ea3y m\u1ed9t m\u00ecnh v\u1edbi n\u0103ng su\u1ea5t g\u1ea5p \u0111\u00f4i trong $\\dfrac{7}{2}$ gi\u1edd \u0111\u01b0\u1ee3c $2.\\dfrac{7}{2y}=\\dfrac{7}{y}$ b\u1ec3.<br\/> Khi \u0111\u00f3 c\u00f2n $\\dfrac{1}{3}$ b\u1ec3 th\u00ec \u0111\u1ea7y n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{7}{y}=\\dfrac{1}{3}$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh: $\\left\\{ \\begin{aligned} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{12} \\\\ & \\dfrac{7}{y}=\\dfrac{1}{3} \\\\ \\end{aligned} \\right.$ <br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & \\dfrac{1}{x}+\\dfrac{1}{y}=\\dfrac{1}{12} \\\\ & y=21 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & \\dfrac{1}{x}+\\dfrac{1}{21}=\\dfrac{1}{12} \\\\ & y=21 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x=28 \\\\ & y=21 \\\\ \\end{aligned} \\right.$(th\u1ecfa m\u00e3n). <br\/>V\u1eady v\u00f2i I ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3 trong $28$ gi\u1edd, v\u00f2i II ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3 trong $21$ gi\u1edd.<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 l\u00e0 $28$ v\u00e0 $21$<\/span><\/span>"}]}],"id_ques":338},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>N\u0103m ngo\u00e1i, hai \u0111\u01a1n v\u1ecb s\u1ea3n xu\u1ea5t n\u00f4ng nghi\u1ec7p thu ho\u1ea1ch $720$ t\u1ea5n th\u00f3c. N\u0103m nay, \u0111\u01a1n v\u1ecb th\u1ee9 I l\u00e0m v\u01b0\u1ee3t m\u1ee9c $15\\%,$ \u0111\u01a1n v\u1ecb th\u1ee9 II l\u00e0m v\u01b0\u1ee3t m\u1ee9c $12\\%$ so v\u1edbi n\u0103m ngo\u00e1i. Do \u0111\u00f3 c\u1ea3 2 \u0111\u01a1n v\u1ecb thu ho\u1ea1ch \u0111\u01b0\u1ee3c $819$ t\u1ea5n th\u00f3c. H\u1ecfi n\u0103m ngo\u00e1i, m\u1ed7i \u0111\u01a1n v\u1ecb thu ho\u1ea1ch \u0111\u01b0\u1ee3c bao nhi\u00eau t\u1ea5n th\u00f3c?<\/span>","select":["A. \u0110\u01a1n v\u1ecb I thu ho\u1ea1ch \u0111\u01b0\u1ee3c 300 t\u1ea5n, \u0111\u01a1n v\u1ecb II thu ho\u1ea1ch \u0111\u01b0\u1ee3c 420 t\u1ea5n ","B. \u0110\u01a1n v\u1ecb I thu ho\u1ea1ch \u0111\u01b0\u1ee3c 420 t\u1ea5n, \u0111\u01a1n v\u1ecb II thu ho\u1ea1ch \u0111\u01b0\u1ee3c 300 t\u1ea5n ","C. \u0110\u01a1n v\u1ecb I thu ho\u1ea1ch \u0111\u01b0\u1ee3c 520 t\u1ea5n, \u0111\u01a1n v\u1ecb II thu ho\u1ea1ch \u0111\u01b0\u1ee3c 200 t\u1ea5n","D. \u0110\u01a1n v\u1ecb I thu ho\u1ea1ch \u0111\u01b0\u1ee3c 200 t\u1ea5n, \u0111\u01a1n v\u1ecb II thu ho\u1ea1ch \u0111\u01b0\u1ee3c 520 t\u1ea5n "],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u1ea3ng ph\u00e2n t\u00edch thu ho\u1ea1ch th\u00f3c c\u1ee7a hai \u0111\u01a1n v\u1ecb:<br\/><table><tr><th><br><\/th><th>\u0110\u01a1n v\u1ecb I (t\u1ea5n)<br><\/th><th>\u0110\u01a1n v\u1ecb II (t\u1ea5n)<br><\/th><th>C\u1ea3 hai \u0111\u01a1n v\u1ecb (t\u1ea5n)<br><\/th><\/tr><tr><th>N\u0103m ngo\u00e1i<br><\/th><td>$x$<\/td><td>$y$<\/td><td>$720$<\/td><\/tr><tr><th>N\u0103m nay<br><\/th><td>$x+15\\%x$<\/td><td>$y+12\\%y$<\/td><td>$819$<\/td><\/tr><\/table><br\/> Ta thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb cho s\u1ed1 t\u1ea5n th\u00f3c m\u00e0 hai \u0111\u01a1n v\u1ecb thu ho\u1ea1ch \u0111\u01b0\u1ee3c n\u0103m ngo\u00e1i v\u00e0 n\u0103m nay.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi $x$ l\u00e0 s\u1ed1 t\u1ea5n th\u00f3c \u0111\u01a1n v\u1ecb I thu ho\u1ea1ch \u0111\u01b0\u1ee3c n\u0103m ngo\u00e1i; $y$ l\u00e0 s\u1ed1 t\u1ea5n th\u00f3c \u0111\u01a1n v\u1ecb II thu ho\u1ea1ch \u0111\u01b0\u1ee3c n\u0103m ngo\u00e1i $ (0 < x, y < 720) $ <br\/>N\u0103m ngo\u00e1i, hai \u0111\u01a1n v\u1ecb s\u1ea3n xu\u1ea5t n\u00f4ng nghi\u1ec7p thu ho\u1ea1ch $720$ t\u1ea5n th\u00f3c n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x+y=720$ (1)<br\/>N\u0103m nay \u0111\u01a1n v\u1ecb I l\u00e0m v\u01b0\u1ee3t m\u1ee9c $15\\%$ n\u00ean \u0111\u01a1n v\u1ecb I s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c $x+\\dfrac{15}{100}x=1,15x$ t\u1ea5n <br\/> \u0110\u01a1n v\u1ecb II l\u00e0m v\u01b0\u1ee3t m\u1ee9c $12\\% $ n\u00ean \u0111\u01a1n v\u1ecb II s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c $y+\\dfrac{12}{100}y=1,12y$ t\u1ea5n<br\/>V\u00ec c\u1ea3 2 \u0111\u01a1n v\u1ecb thu ho\u1ea1ch \u0111\u01b0\u1ee3c $819$ t\u1ea5n th\u00f3c n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $1,15x+1,12y=819$ (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh $\\left\\{ \\begin{aligned} & 1,15x+1,12y=819 \\\\ & x+y=720 \\\\ \\end{aligned} \\right.$<br\/>$\\Leftrightarrow \\left\\{ \\begin{aligned} & 1,15\\left( 720-y \\right)+1,12y=819 \\\\ & x=720-y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & -0,03y=-9 \\\\ & x=720-y \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & y=300 \\\\ & x=420 \\\\ \\end{aligned} \\right.$<br\/>V\u1eady n\u0103m ngo\u00e1i, \u0111\u01a1n v\u1ecb I thu ho\u1ea1ch \u0111\u01b0\u1ee3c $420$ t\u1ea5n th\u00f3c, \u0111\u01a1n v\u1ecb II thu ho\u1ea1ch \u0111\u01b0\u1ee3c $300$ t\u1ea5n th\u00f3c.<br\/><span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B <\/span><\/span>","column":1}]}],"id_ques":339},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["70"],["50"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>Trong m\u1ed9t bu\u1ed5i d\u1ea1 h\u1ed9i, s\u1ed1 h\u1ecdc sinh nam nhi\u1ec1u h\u01a1n s\u1ed1 h\u1ecdc sinh n\u1eef l\u00e0 $20$ em. Trong khi khi\u00eau v\u0169 c\u00f3 $40$ b\u1ea1n nam v\u00e0 $40$ b\u1ea1n n\u1eef \u0111ang tr\u00ean s\u00e0n nh\u1ea3y. S\u1ed1 b\u1ea1n nam kh\u00f4ng nh\u1ea3y g\u1ea5p ba s\u1ed1 b\u1ea1n n\u1eef kh\u00f4ng nh\u1ea3y. H\u1ecfi c\u00f3 bao nhi\u00eau b\u1ea1n nam v\u00e0 b\u1ea1n n\u1eef d\u1ef1 d\u1ea1 h\u1ed9i? <br\/><b> \u0110\u00e1p s\u1ed1: <\/b>S\u1ed1 b\u1ea1n nam d\u1ef1 d\u1ea1 h\u1ed9i l\u00e0 _input_, s\u1ed1 b\u1ea1n n\u1eef d\u1ef1 d\u1ea1 h\u1ed9i l\u00e0 _input_<\/span>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: L\u1eadp h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>+ G\u1ecdi \u1ea9n l\u00e0 s\u1ed1 b\u1ea1n nam v\u00e0 s\u1ed1 b\u1ea1n n\u1eef tham gia d\u1ea1 h\u1ed9i<br\/>+ T\u1eeb gi\u1ea3i thi\u1ebft th\u1ee9 nh\u1ea5t, ta l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb s\u1ef1 ch\u00eanh l\u1ec7ch gi\u1eefa s\u1ed1 nam v\u00e0 s\u1ed1 n\u1eef<br\/>+ T\u1eeb gi\u1ea3 thi\u1ebft th\u1ee9 hai, l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb s\u1ed1 b\u1ea1n nam v\u00e0 n\u1eef kh\u00f4ng tham gia nh\u1ea3y. <br\/>B\u01b0\u1edbc 2: Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh v\u1eeba l\u1eadp.<br\/>B\u01b0\u1edbc 3: Ki\u1ec3m tra nghi\u1ec7m c\u00f3 th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n kh\u00f4ng v\u00e0 k\u1ebft lu\u1eadn b\u00e0i to\u00e1n <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi s\u1ed1 b\u1ea1n nam d\u1ef1 d\u1ea1 h\u1ed9i l\u00e0 $x$ v\u00e0 s\u1ed1 b\u1ea1n n\u1eef d\u1ef1 d\u1ea1 h\u1ed9i l\u00e0 $y$ v\u1edbi $x,y$ nguy\u00ean d\u01b0\u01a1ng <br\/>V\u00ec s\u1ed1 nam nhi\u1ec1u h\u01a1n s\u1ed1 n\u1eef l\u00e0 $20$ b\u1ea1n n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: ph\u01b0\u01a1ng tr\u00ecnh : $x - y= 20$<br\/>S\u1ed1 nam kh\u00f4ng nh\u1ea3y l\u00e0 $x \u2013 40$ (b\u1ea1n)<br\/>S\u1ed1 n\u1eef kh\u00f4ng nh\u1ea3y l\u00e0 $y - 40$ (b\u1ea1n) <br\/>S\u1ed1 b\u1ea1n nam kh\u00f4ng nh\u1ea3y g\u1ea5p ba s\u1ed1 b\u1ea1n n\u1eef kh\u00f4ng nh\u1ea3y n\u00ean: $x \u201340=3(y-40)$<br\/>Ta c\u00f3 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:$\\left\\{ \\begin{align} & x-y=20 \\\\ & x-40=3\\left( y-40 \\right) \\\\ \\end{align} \\right.$<br\/> $\\Leftrightarrow \\left\\{ \\begin{aligned} & x-y=20 \\\\ & x-3y=-80 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned} & x-y=20 \\\\ & 2y=100 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left\\{ \\begin{aligned}& x=70 \\\\ & y=50 \\\\ \\end{aligned} \\right.$<br\/>V\u1eady c\u00f3 $70$ b\u1ea1n nam v\u00e0 $50$ b\u1ea1n n\u1eef tham gia d\u1ea1 h\u1ed9i.<br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 l\u00e0 $70$ v\u00e0 $50$<\/span><\/span>"}]}],"id_ques":340}],"lesson":{"save":0,"level":2}}