{"segment":[{"time":9,"part":[{"time":3,"title":"Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh","title_trans":"S\u1eafp x\u1ebfp c\u00e1c \u00fd \u0111\u1ec3 \u0111\u01b0\u1ee3c c\u00e2u tr\u1ea3 l\u1eddi \u0111\u00fang.","temp":"sequence","correct":[[[3],[5],[2],[1],[4]]],"list":[{"point":10,"image":"","left":["L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb t\u01b0\u01a1ng quan gi\u1eefa \u1ea9n s\u1ed1 v\u00e0 c\u00e1c d\u1eef ki\u1ec7n \u0111\u00e3 bi\u1ebft","\u0110\u1ed1i chi\u1ebfu nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (n\u1ebfu c\u00f3) v\u1edbi \u0111i\u1ec1u ki\u1ec7n c\u1ee7a \u1ea9n s\u1ed1 v\u00e0 v\u1edbi \u0111\u1ec1 b\u00e0i \u0111\u1ec3 tr\u1ea3 l\u1eddi","Bi\u1ec3u th\u1ecb c\u00e1c d\u1eef ki\u1ec7n ch\u01b0a bi\u1ebft qua \u1ea9n s\u1ed1","Ch\u1ecdn \u1ea9n s\u1ed1 v\u00e0 n\u00eau \u0111i\u1ec1u ki\u1ec7n th\u00edch h\u1ee3p c\u1ee7a \u1ea9n s\u1ed1","Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh v\u1eeba l\u1eadp"],"top":70,"hint":"","explain":"<span class='basic_left'><b> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i b\u00e0i to\u00e1n b\u1eb1ng c\u00e1ch l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh: <\/b><br\/><i>B\u01b0\u1edbc 1:<\/i> L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh<br\/>+ Ch\u1ecdn \u1ea9n s\u1ed1 v\u00e0 n\u00eau \u0111i\u1ec1u ki\u1ec7n th\u00edch h\u1ee3p c\u1ee7a \u1ea9n s\u1ed1;<br\/>+ Bi\u1ec3u th\u1ecb c\u00e1c d\u1eef ki\u1ec7n ch\u01b0a bi\u1ebft qua \u1ea9n s\u1ed1;<br\/>+ L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb t\u01b0\u01a1ng quan gi\u1eefa \u1ea9n s\u1ed1 v\u00e0 c\u00e1c d\u1eef ki\u1ec7n \u0111\u00e3 bi\u1ebft<br\/><i>B\u01b0\u1edbc 2:<\/i> Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh v\u1eeba l\u1eadp.<br\/><i>B\u01b0\u1edbc 3:<\/i> \u0110\u1ed1i chi\u1ebfu nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh (n\u1ebfu c\u00f3) v\u1edbi \u0111i\u1ec1u ki\u1ec7n c\u1ee7a \u1ea9n s\u1ed1 v\u00e0 v\u1edbi \u0111\u1ec1 b\u00e0i \u0111\u1ec3 tr\u1ea3 l\u1eddi.<br\/><span class='basic_green'>L\u01b0u \u00fd:<\/span> Khi ch\u1ecdn \u1ea9n \u0111\u1ec3 l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh, th\u00f4ng th\u01b0\u1eddng ta th\u01b0\u1eddng ch\u1ecdn \u0111\u1ea1i l\u01b0\u1ee3ng c\u1ea7n t\u00ecm l\u00e0 \u1ea9n s\u1ed1.<\/span>"}]}],"id_ques":971},{"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'>T\u00ecm m\u1ed9t s\u1ed1 bi\u1ebft r\u1eb1ng s\u1ed1 \u0111\u00f3 nh\u1ecf h\u01a1n ngh\u1ecbch \u0111\u1ea3o c\u1ee7a n\u00f3 l\u00e0 $2,1.$ N\u1ebfu g\u1ecdi s\u1ed1 \u0111\u00f3 l\u00e0 $x$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh l\u1eadp \u0111\u01b0\u1ee3c l\u00e0:","select":["A. $x-\\dfrac{1}{x}=2,1$ ","B. $\\dfrac{1}{x}-x=2,1$ ","C. $\\dfrac{1}{x}+x=2,1$ ","D. $|x|-x=2,1$"],"hint":"","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 $x.$ Khi \u0111\u00f3 ngh\u1ecbch \u0111\u1ea3o c\u1ee7a n\u00f3 l\u00e0 $\\dfrac{1}{x},$ $x\\ne 0$ <br\/>V\u00ec s\u1ed1 \u0111\u00f3 nh\u1ecf h\u01a1n ngh\u1ecbch \u0111\u1ea3o c\u1ee7a n\u00f3 l\u00e0 $2,1$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{1}{x}-x=2,1$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":4}]}],"id_ques":972},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o c\u00e1c \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["5"],["6"]]],"list":[{"point":5,"width":60,"type_input":"","ques":"<span class='basic_left'>T\u00ecm hai s\u1ed1 bi\u1ebft t\u1ed5ng c\u1ee7a ch\u00fang b\u1eb1ng $11$ v\u00e0 t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a ch\u00fang b\u1eb1ng $61.$<br\/>Hai s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 _input_ v\u00e0 _input_","hint":"","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 th\u1ee9 nh\u1ea5t l\u00e0 $x$.<br\/>V\u00ec t\u1ed5ng hai s\u1ed1 l\u00e0 $11$ n\u00ean s\u1ed1 th\u1ee9 hai l\u00e0 $11-x$<br\/>Do t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a hai s\u1ed1 b\u1eb1ng $61$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & {{x}^{2}}+{{\\left( 11-x \\right)}^{2}}=61 \\\\ & \\Leftrightarrow {{x}^{2}}+121-22x+{{x}^{2}}=61 \\\\ & \\Leftrightarrow 2{{x}^{2}}-22x+60=0 \\\\ & \\Leftrightarrow {{x}^{2}}-11x+30=0 \\\\ \\end{align}$ <br\/>$\\Delta ={{11}^{2}}-4.30=1$ <br\/>Suy ra ${{x}_{1}}=\\dfrac{11+1}{2}=6$; ${{x}_{2}}=\\dfrac{11-1}{2}=5$ <br\/>V\u1eady hai s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 $5$ v\u00e0 $6.$<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $5;$ $6.$<\/span><\/span>"}]}],"id_ques":973},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'>T\u00edch c\u1ee7a hai s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp l\u1edbn h\u01a1n t\u1ed5ng c\u1ee7a ch\u00fang l\u00e0 $55.$ Hai s\u1ed1 \u0111\u00f3 l\u00e0","select":["A. $7$ v\u00e0 $8$","B. $6$ v\u00e0 $7$","C. $8$ v\u00e0 $9$","D. $9$ v\u00e0 $10$"],"hint":"","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 b\u00e9 l\u00e0 $x$ th\u00ec s\u1ed1 li\u1ec1n k\u1ec1 sau l\u00e0 $x+1,$$x\\in \\mathbb{N}$ <br\/>T\u00edch c\u1ee7a hai s\u1ed1 l\u00e0 $x(x+1);$ t\u1ed5ng c\u1ee7a hai s\u1ed1 l\u00e0 $x+x+1=2x+1$<br\/>V\u00ec t\u00edch c\u1ee7a hai s\u1ed1 l\u1edbn h\u01a1n t\u1ed5ng c\u1ee7a ch\u00fang l\u00e0 $55$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: <br\/>$\\begin{align} & x\\left( x+1 \\right)-\\left( 2x+1 \\right)=55 \\\\ & \\Leftrightarrow {{x}^{2}}+x-2x-1=55 \\\\ & \\Leftrightarrow {{x}^{2}-x-56}=0 \\\\ & \\Delta=225 \\Rightarrow \\sqrt{\\Delta}=15 \\\\ & \\Rightarrow x_1=\\dfrac{1+15}{2}=8;x_2=\\dfrac{1-15}{2}=-7 \\\\ \\end{align}$<br\/>V\u00ec $x\\in \\mathbb{N}$ n\u00ean $x=x_1=8$<br\/> V\u1eady hai s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $8$ v\u00e0 $9.$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":974},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["9"],["11"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"T\u00ecm hai s\u1ed1 t\u1ef1 nhi\u00ean l\u1ebb li\u00ean ti\u1ebfp bi\u1ebft r\u1eb1ng t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a ch\u00fang b\u1eb1ng $202.$<br\/>Hai s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 _input_ v\u00e0 _input_","hint":"S\u1ed1 t\u1ef1 nhi\u00ean l\u1ebb c\u00f3 d\u1ea1ng $2n+1$ v\u1edbi $n \\in \\mathbb{N}$","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 t\u1ef1 nhi\u00ean l\u1ebb b\u00e9 h\u01a1n l\u00e0 $2n+1$ th\u00ec s\u1ed1 t\u1ef1 nhi\u00ean l\u1ebb k\u1ebf ti\u1ebfp l\u00e0 $2n+3,$ $n\\in \\mathbb{N}$ <br\/>V\u00ec t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a ch\u00fang b\u1eb1ng $202$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,{{\\left( 2n+1 \\right)}^{2}}+{{\\left( 2n+3 \\right)}^{2}}=202 \\\\ & \\Leftrightarrow 4{{n}^{2}}+4n+1+4{{n}^{2}}+12n+9=202 \\\\ & \\Leftrightarrow 8{{n}^{2}}+16n-192=0 \\\\ & \\Leftrightarrow {{n}^{2}}+2n-24=0 \\\\ \\end{align}$ <br\/>$\\Delta '=25$ <br\/>Suy ra $n=4$ ho\u1eb7c $n=-6$. <br\/>V\u00ec $n\\in \\mathbb{N}$ n\u00ean $n=4$<br\/>Suy ra $2n+1=9$ v\u00e0 $2n+3=11$ <br\/>V\u1eady hai s\u1ed1 t\u1ef1 nhi\u00ean l\u1ebb li\u00ean ti\u1ebfp l\u1ea7n l\u01b0\u1ee3t l\u00e0 $9$ v\u00e0 $11.$<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $9$ v\u00e0 $11.$ <\/span><\/span>"}]}],"id_ques":975},{"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 m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1 bi\u1ebft t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 b\u1eb1ng $13$ v\u00e0 n\u1ebfu c\u1ed9ng $34 $ v\u00e0o t\u00edch hai ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 th\u00ec ta \u0111\u01b0\u1ee3c ch\u00ednh s\u1ed1 \u0111\u00f3.<br\/>S\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0:","select":["A. $85$","B. $58$","C. $67$","D. $76$"],"hint":"S\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1 c\u00f3 d\u1ea1ng $10a+b$ trong \u0111\u00f3 $a$ v\u00e0 $b$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c v\u00e0 h\u00e0ng \u0111\u01a1n v\u1ecb.","explain":"<span class='basic_left'>G\u1ecdi ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c l\u00e0 $x$ th\u00ec ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $13-x.$ \u0110i\u1ec1u ki\u1ec7n: $ 0< x \\le 9 $ v\u00e0 $ x \\in \\mathbb{N}$ <br\/>Khi \u0111\u00f3 s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 $10x+(13-x)=9x+13$<br\/>N\u1ebfu c\u1ed9ng $34$ v\u00e0o t\u00edch hai ch\u1eef s\u1ed1 c\u1ee7a s\u1ed1 t\u1ef1 nhi\u00ean th\u00ec \u0111\u01b0\u1ee3c ch\u00ednh s\u1ed1 \u0111\u00f3 n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & x\\left( 13-x \\right)+34=9x+13 \\\\ & \\Leftrightarrow 13x-{{x}^{2}}+34=9x+13 \\\\ & \\Leftrightarrow {{x}^{2}}-4x-21=0 \\\\ \\end{align}$ <br\/>$\\Delta '=25$ <br\/>Suy ra ${{x}_{1}}=7$ (th\u1ecfa m\u00e3n);${{x}_{2}}=-3$ (lo\u1ea1i)<br\/>Suy ra ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c l\u00e0 $7;$ ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $6$<br\/>V\u1eady s\u1ed1 t\u1ef1 nhi\u00ean c\u1ea7n t\u00ecm l\u00e0 $76$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span><\/span>","column":4}]}],"id_ques":976},{"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":[[1]],"list":[{"point":5,"ques":"<span class='basic_left'>Hai ng\u01b0\u1eddi c\u00f9ng \u0111i qu\u00e3ng \u0111\u01b0\u1eddng $AB$ d\u00e0i $450$ $km$ v\u00e0 kh\u1edfi h\u00e0nh c\u00f9ng m\u1ed9t l\u00fac. V\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u00edt h\u01a1n v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $30$ $km\/h$ n\u00ean ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u0111\u1ebfn $B$ sau ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $4$ gi\u1edd.<br\/><b>C\u00e2u 1:<\/b> N\u1ebfu g\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0 $x$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh l\u1eadp \u0111\u01b0\u1ee3c l\u00e0:","select":["A. $\\dfrac{450}{x}-\\dfrac{450}{x+30}=4$ ","B. $\\dfrac{450}{x}-\\dfrac{450}{x-30}=4$ ","C. $\\dfrac{450}{x-30}-\\dfrac{450}{x}=4$ "],"hint":"C\u00f4ng th\u1ee9c: $s=vt$ trong \u0111\u00f3 $s$ l\u00e0 qu\u00e3ng \u0111\u01b0\u1eddng \u0111i \u0111\u01b0\u1ee3c trong th\u1eddi gian $t$ v\u1edbi v\u1eadn t\u1ed1c $v$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u1ea3ng ph\u00e2n t\u00edch chuy\u1ec3n \u0111\u1ed9ng: <br\/> <table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>V\u1eadn t\u1ed1c $(km\/h)$<br><\/th><th>Qu\u00e3ng \u0111\u01b0\u1eddng $(km)$<br><\/th><th>Th\u1eddi gian (gi\u1edd)<br><\/th><\/tr><tr><th>Ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t<br><\/th><td>$x$<\/td><td>$450$<\/td><td>$\\dfrac{450}{x}$<\/td><\/tr><tr><th>Ng\u01b0\u1eddi th\u1ee9 hai<br><\/th><td>$x+30$<\/td><td>$450$<\/td><td>$\\dfrac{450}{x+30}$<\/td><\/tr><\/table><br\/>L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb m\u1ed1i quan h\u1ec7 v\u1ec1 th\u1eddi gian c\u1ee7a hai ng\u01b0\u1eddi.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0 $x$ $(km\/h),$ $x>0$.<br\/> V\u00ec v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u00edt h\u01a1n v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $30$ $km\/h$ n\u00ean v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $x+30$ $(km\/h).$ <br\/>Th\u1eddi gian ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u0111i \u0111\u01b0\u1ee3c l\u00e0 $\\dfrac{450}{x}$ (gi\u1edd) v\u00e0 th\u1eddi gian \u0111i c\u1ee7a ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $\\dfrac{450}{x+30}$ (gi\u1edd).<br\/>Do ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u0111\u1ebfn $B$ sau ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $4$ gi\u1edd n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{450}{x}-\\dfrac{450}{x+30}=4$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":3}]}],"id_ques":977},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["10"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>Hai ng\u01b0\u1eddi c\u00f9ng \u0111i qu\u00e3ng \u0111\u01b0\u1eddng $AB$ d\u00e0i $450$ $km$ v\u00e0 c\u00f9ng kh\u1edfi h\u00e0nh m\u1ed9t l\u00fac. V\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u00edt h\u01a1n v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $30$ $km\/h$ n\u00ean ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u0111\u1ebfn $B$ sau ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $4$ gi\u1edd.<br\/><b>C\u00e2u 2:<\/b> Th\u1eddi gian ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u0111i qu\u00e3ng \u0111\u01b0\u1eddng $AB$ l\u00e0 _input_ (gi\u1edd) <\/span>","hint":"S\u1eed d\u1ee5ng k\u1ebft qu\u1ea3 c\u00e2u 1, ta x\u00e1c \u0111\u1ecbnh v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t. T\u1eeb \u0111\u00f3 x\u00e1c \u0111\u1ecbnh th\u1eddi gian.","explain":"<span class='basic_left'>G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0 $x$ $(km\/h),$ $x>0$.<br\/> V\u00ec v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u00edt h\u01a1n v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $30$ $km\/h$ n\u00ean v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $x+30$ $(km\/h).$ <br\/>Th\u1eddi gian ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u0111i \u0111\u01b0\u1ee3c l\u00e0 $\\dfrac{450}{x}$ (gi\u1edd) v\u00e0 th\u1eddi gian \u0111i c\u1ee7a ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $\\dfrac{450}{x+30}$ (gi\u1edd).<br\/>Do ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u0111\u1ebfn $B$ sau ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $4$ gi\u1edd n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,\\,\\dfrac{450}{x}-\\dfrac{450}{x+30}=4 \\\\ & \\Rightarrow 450\\left( x+30 \\right)-450x=4x\\left( x+30 \\right) \\\\ & \\Leftrightarrow 13500=4{{x}^{2}}+120x \\\\ & \\Leftrightarrow {{x}^{2}}+30x-3375=0 \\\\ \\end{align}$ <br\/>$\\Delta '=3600$ <br\/>Suy ra ${{x}_{1}}=45;{{x}_{2}}=-75$ <br\/>V\u00ec $x>0$ n\u00ean $ x=45$<br\/>V\u1eady v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0 $45$ $km\/h.$<br\/>Th\u1eddi gian ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u0111i qu\u00e3ng \u0111\u01b0\u1eddng $AB$ l\u00e0 $\\dfrac{450}{45}=10$ (gi\u1edd)<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 $10.$ <\/span><\/span>"}]}],"id_ques":978},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"M\u1ed9t ng\u01b0\u1eddi \u0111i xe m\u00e1y t\u1eeb $A$ \u0111\u1ebfn $B$ v\u1edbi v\u1eadn t\u1ed1c l\u00e0 $30$ $km\/h.$ Khi \u0111\u1ebfn $B$ ng\u01b0\u1eddi \u0111\u00f3 ngh\u1ec9 $20$ ph\u00fat r\u1ed3i quay tr\u1edf v\u1ec1 $A$ v\u1edbi v\u1eadn t\u1ed1c $25km\/h.$ Bi\u1ebft th\u1eddi gian c\u1ea3 \u0111i l\u1eabn v\u1ec1 l\u00e0 $5$ gi\u1edd $50$ ph\u00fat.<br\/>Khi \u0111\u00f3 qu\u00e3ng \u0111\u01b0\u1eddng $AB$ c\u00f3 \u0111\u1ed9 d\u00e0i l\u00e0:","select":["A. $70$ $(km)$ ","B. $80$ $(km)$ ","C. $75$ $(km)$ ","D. $85$ $(km)$ "],"hint":"","explain":"<span class='basic_left'>\u0110\u1ed5i $20$ ph\u00fat $=\\dfrac{1}{3}$ gi\u1edd; $5$ gi\u1edd $50$ ph\u00fat $=\\dfrac{35}{6}$ gi\u1edd<br\/>G\u1ecdi qu\u00e3ng \u0111\u01b0\u1eddng $AB$ l\u00e0 $x$ $(km),$$x>0$<br\/>Th\u1eddi gian \u0111i t\u1eeb $A$ \u0111\u1ebfn $B$ l\u00e0 $\\dfrac{x}{30}$(gi\u1edd), th\u1eddi gian \u0111i t\u1eeb $B$ \u0111\u1ebfn $A$ l\u00e0 $\\dfrac{x}{25}$ (gi\u1edd)<br\/>Do ng\u01b0\u1eddi \u0111\u00f3 c\u00f3 ngh\u1ec9 $\\dfrac{1}{3}$ gi\u1edd v\u00e0 th\u1eddi gian c\u1ea3 \u0111i l\u1eabn v\u1ec1 l\u00e0 $\\dfrac{35}{6}$ gi\u1edd n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/> $\\begin{align} & \\dfrac{x}{30}+\\dfrac{1}{3}+\\dfrac{x}{25}=\\dfrac{35}{6} \\\\ & \\Leftrightarrow 5x+6x=825 \\\\ & \\Leftrightarrow x=75 \\\\ \\end{align}$<br\/> V\u1eady \u0111\u1ed9 d\u00e0i qu\u00e3ng \u0111\u01b0\u1eddng $AB$ l\u00e0 $75$ $km$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C <\/span><\/span>","column":4}]}],"id_ques":979},{"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":[[1]],"list":[{"point":5,"ques":"<span class='basic_left'>M\u1ed9t ca n\u00f4 xu\u00f4i d\u00f2ng m\u1ed9t kh\u00fac s\u00f4ng d\u00e0i $50$ $km$ r\u1ed3i ng\u01b0\u1ee3c kh\u00fac s\u00f4ng \u1ea5y $32$ $km$ th\u00ec h\u1ebft $4$ gi\u1edd $30$ ph\u00fat. Bi\u1ebft v\u1eadn t\u1ed1c th\u1ef1c c\u1ee7a ca n\u00f4 b\u1eb1ng $18$ $km\/h$. Khi \u0111\u00f3 v\u1eadn t\u1ed1c d\u00f2ng n\u01b0\u1edbc l\u00e0:","select":["A. $2$ $(km\/h)$ ","B. $2,5$ $(km\/h)$ ","C. $3$ $(km\/h)$ ","D. $3,5$ $(km\/h)$"],"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 $\u2013$ 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\/>B\u1ea3ng ph\u00e2n t\u00edch chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a ca n\u00f4: <br\/> <table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>V\u1eadn t\u1ed1c $(km\/h)$<br><\/th><th>Qu\u00e3ng \u0111\u01b0\u1eddng $(km)$<br><\/th><th>Th\u1eddi gian (gi\u1edd)<br><\/th><\/tr><tr><th>Xu\u00f4i d\u00f2ng<br><\/th><td>$18+x$<\/td><td>$50$<\/td><td>$\\dfrac{50}{x+18}$<\/td><\/tr><tr><th>Ng\u01b0\u1ee3c d\u00f2ng<br><\/th><td>$18-x$<\/td><td>$32$<\/td><td>$\\dfrac{32}{18-x}$<\/td><\/tr><\/table><br\/>L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb m\u1ed1i quan h\u1ec7 v\u1ec1 th\u1eddi gian c\u1ee7a ca n\u00f4.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>\u0110\u1ed5i $4$ gi\u1edd $30$ ph\u00fat $=\\dfrac{9}{2}$ gi\u1edd<br\/>G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a d\u00f2ng n\u01b0\u1edbc l\u00e0 $x$ $(km\/h)$<br\/>Khi \u0111\u00f3 v\u1eadn t\u1ed1c khi xu\u00f4i d\u00f2ng l\u00e0 $x+18$ $(km\/h),$ v\u1eadn t\u1ed1c ng\u01b0\u1ee3c d\u00f2ng l\u00e0 $18-x$ $(km\/h).$ \u0110i\u1ec1u ki\u1ec7n $ 0 < x < 18 $ <br\/>Do ca n\u00f4 \u0111i xu\u00f4i d\u00f2ng $50$ $km$ n\u00ean th\u1eddi gian ca n\u00f4 xu\u00f4i d\u00f2ng l\u00e0 $\\dfrac{50}{x+18}$ (gi\u1edd) <br\/>Do ca n\u00f4 \u0111i ng\u01b0\u1ee3c d\u00f2ng $32$ $km$ n\u00ean th\u1eddi gian khi ca n\u00f4 ng\u01b0\u1ee3c d\u00f2ng l\u00e0 $\\dfrac{32}{18-x}$ (gi\u1edd)<br\/>Th\u1eddi gian c\u1ea3 \u0111i l\u1eabn v\u1ec1 t\u1ed5ng c\u1ed9ng h\u1ebft $4$ gi\u1edd $30$ ph\u00fat n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\dfrac{50}{x+18}+\\dfrac{32}{18-x}=\\dfrac{9}{2} \\\\ & \\Rightarrow 50.2\\left( 18-x \\right)+32.2.\\left( x+18 \\right)=9\\left( x+18 \\right)\\left( 18-x \\right) \\\\ & \\Leftrightarrow 2952-36x=9\\left( {{18}^{2}}-{{x}^{2}} \\right) \\\\ & \\Leftrightarrow 9{{x}^{2}}-36x+36=0 \\\\ & \\Leftrightarrow {{\\left( 3x-6 \\right)}^{2}}=0 \\\\ & \\Leftrightarrow 3x-6=0 \\\\ & \\Leftrightarrow x=2 \\,(\\text{th\u1ecfa m\u00e3n}) \\\\ \\end{align}$ <br\/>V\u1eady v\u1eadn t\u1ed1c c\u1ee7a d\u00f2ng n\u01b0\u1edbc l\u00e0 $2$ $km\/h.$<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":4}]}],"id_ques":980},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["50"],["40"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>Qu\u00e3ng \u0111\u01b0\u1eddng $AB$ d\u00e0i $100$ $km.$ Hai xe \u00f4 t\u00f4 kh\u1edfi h\u00e0nh c\u00f9ng m\u1ed9t l\u00fac t\u1eeb $A$ \u0111\u1ebfn $B.$ V\u1eadn t\u1ed1c c\u1ee7a xe th\u1ee9 nh\u1ea5t l\u1edbn h\u01a1n v\u1eadn t\u1ed1c c\u1ee7a xe th\u1ee9 hai l\u00e0 $10$ $km\/h$ n\u00ean xe th\u1ee9 nh\u1ea5t \u0111\u1ebfn $B$ s\u1edbm h\u01a1n xe th\u1ee9 hai l\u00e0 $30$ ph\u00fat. T\u00ednh v\u1eadn t\u1ed1c m\u1ed7i xe.<br\/><b>\u0110\u00e1p s\u1ed1:<\/b> V\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 th\u1ee9 nh\u1ea5t l\u00e0 _input_ $(km\/h)$; v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 th\u1ee9 hai l\u00e0 _input_$(km\/h)$<\/span>","hint":"","explain":"<span class='basic_left'>\u0110\u1ed5i $30$ ph\u00fat $=\\dfrac{1}{2}$ gi\u1edd<br\/>G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 th\u1ee9 nh\u1ea5t l\u00e0 $x$ $(km\/h).$<br\/> V\u00ec v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 th\u1ee9 nh\u1ea5t \u00edt h\u01a1n v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 th\u1ee9 hai l\u00e0 $10$ $km\/h$ n\u00ean v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 th\u1ee9 hai l\u00e0 $x-10$ $(km\/h).$ \u0110i\u1ec1u ki\u1ec7n $x>10$<br\/>Do qu\u00e3ng \u0111\u01b0\u1eddng AB d\u00e0i $100$ $km$ n\u00ean th\u1eddi gian ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t \u0111i \u0111\u01b0\u1ee3c l\u00e0 $\\dfrac{100}{x}$ (gi\u1edd) v\u00e0 th\u1eddi gian \u0111i c\u1ee7a ng\u01b0\u1eddi th\u1ee9 hai l\u00e0 $\\dfrac{100}{x-10}$ (gi\u1edd).<br\/>Do xe th\u1ee9 nh\u1ea5t \u0111\u1ebfn $B$ s\u1edbm h\u01a1n xe th\u1ee9 hai l\u00e0 $\\dfrac{1}{2}$ gi\u1edd n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,\\dfrac{100}{x-10}-\\dfrac{100}{x}=\\dfrac{1}{2} \\\\ & \\Rightarrow 100x-100\\left( x-10 \\right)=\\dfrac{1}{2}x\\left( x-10 \\right) \\\\ & \\Leftrightarrow \\dfrac{1}{2}{{x}^{2}}-5x-1000=0 \\\\ & \\Leftrightarrow {{x}^{2}}-10x-2000=0 \\\\ & \\Delta '=2025\\Rightarrow \\sqrt{\\Delta '}=45 \\\\ \\end{align}$ <br\/>Suy ra ${{x}_{1}}=50;{{x}_{2}}=-40$ <br\/>V\u00ec $ x >10 $ n\u00ean $x=x_1=50$<br\/>V\u1eady v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 th\u1ee9 nh\u1ea5t l\u00e0 $50$ $km\/h,$ v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 th\u1ee9 hai l\u00e0 $40$ $km\/h.$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $50$ v\u00e0 $40.$ <\/span><\/span>"}]}],"id_ques":981},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["12"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"M\u1ed9t ng\u01b0\u1eddi \u0111i xe \u0111\u1ea1p t\u1eeb $A$ \u0111\u1ebfn $B$ d\u00e0i $36$ $km.$ L\u00fac v\u1ec1, ng\u01b0\u1eddi \u0111\u00f3 t\u0103ng v\u1eadn t\u1ed1c th\u00eam $3$ $km\/h,$ do \u0111\u00f3 th\u1eddi gian v\u1ec1 \u00edt h\u01a1n th\u1eddi gian \u0111i l\u00e0 $36$ ph\u00fat. T\u00ednh v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi \u0111i xe \u0111\u1ea1p l\u00fac \u0111i.<br\/><b>\u0110\u00e1p s\u1ed1: <\/b> _input_ $(km\/h)$","hint":"","explain":"<span class='basic_left'>\u0110\u1ed5i $36$ ph\u00fat $=\\dfrac{3}{5}$ gi\u1edd<br\/>G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi \u0111i xe \u0111\u1ea1p l\u00fac \u0111i l\u00e0 $x$ $(km\/h),$ $x>0$<br\/> V\u00ec l\u00fac v\u1ec1, ng\u01b0\u1eddi \u0111\u00f3 t\u0103ng v\u1eadn t\u1ed1c th\u00eam $3$ $km\/h$ n\u00ean v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi \u0111i xe \u0111\u1ea1p l\u00fac v\u1ec1 l\u00e0 $x+3$ $(km\/h).$<br\/>Do qu\u00e3ng \u0111\u01b0\u1eddng $AB$ d\u00e0i $36$$km$ n\u00ean th\u1eddi gian l\u00fac \u0111i l\u00e0 $\\dfrac{36}{x}$ (gi\u1edd) v\u00e0 th\u1eddi gian l\u00fac v\u1ec1 l\u00e0 $\\dfrac{36}{x+3}$ (gi\u1edd)<br\/>V\u00ec th\u1eddi gian l\u00fac v\u1ec1 \u00edt h\u01a1n th\u1eddi gian \u0111i l\u00e0 $\\dfrac{3}{5}$ gi\u1edd n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,\\dfrac{36}{x}-\\dfrac{36}{x+3}=\\dfrac{3}{5} \\\\ & \\Rightarrow 5.36\\left( x+3 \\right)-5.36x=3.x\\left( x+3 \\right) \\\\ & \\Leftrightarrow 540=3{{x}^{2}}+9x \\\\ & \\Leftrightarrow 3{{x}^{2}}+9x-540=0 \\\\ & \\Leftrightarrow {{x}^{2}}+3x-180=0 \\\\ & \\Delta =729\\Rightarrow \\sqrt{\\Delta }=27 \\\\ \\end{align}$ <br\/>Suy ra ${{x}_{1}}=12;{{x}_{2}}=-15$ <br\/>V\u00ec $x>0$ n\u00ean $x=12$<br\/>V\u1eady v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi \u0111i xe \u0111\u1ea1p l\u00fac \u0111i l\u00e0 $12$ $(km\/h)$<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $12.$ <\/span><\/span>"}]}],"id_ques":982},{"time":24,"part":[{"title":"Ch\u1ecdn <u>nh\u1eefng<\/u> \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"Ch\u1ecdn \u0111\u01b0\u1ee3c nhi\u1ec1u \u0111\u00e1p \u00e1n","temp":"checkbox","correct":[["1","3"]],"list":[{"point":5,"img":"","ques":"M\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 chu vi $110$ $m,$ di\u1ec7n t\u00edch $700$ $m^2.$ G\u1ecdi chi\u1ec1u d\u00e0i c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $x$ $(m)$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh l\u1eadp \u0111\u01b0\u1ee3c l\u00e0:","hint":"Cho h\u00ecnh ch\u1eef nh\u1eadt v\u1edbi k\u00edch th\u01b0\u1edbc $a$ v\u00e0 $b.$ Khi \u0111\u00f3:<br\/>Chu vi h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $2(a+b)$. <br\/>Di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $ab$","column":2,"number_true":2,"select":["A. $x(55-x)=700$","B. $\\left( \\dfrac{700}{x}+x \\right)=110$ ","C. $2\\left( \\dfrac{700}{x}+x \\right)=110$ ","D. $x(110-x)=700$"],"explain":"<span class='basic_left'><b>C\u00e1ch 1:<\/b><br\/>Chu vi h\u00ecnh ch\u1eef nh\u1eadt $110$ $m$ n\u00ean n\u1eeda chu vi l\u00e0 $55$ $m$ hay t\u1ed5ng chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng l\u00e0 $55$ $m.$<br\/>G\u1ecdi chi\u1ec1u d\u00e0i h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $x$ $(m)$ th\u00ec chi\u1ec1u r\u1ed9ng h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $55-x$ $(m).$ \u0110i\u1ec1u ki\u1ec7n: $ 0 < x < 55 $<br\/>Di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $700$ $m^2$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $x(55-x)=700$<br\/><b>C\u00e1ch 2:<\/b> G\u1ecdi chi\u1ec1u d\u00e0i h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $x$ $(m). $<br\/>Do di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $700$ $m^2$ n\u00ean chi\u1ec1u r\u1ed9ng h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $\\dfrac{700}{x}$ $(m)$<br\/>V\u00ec h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 chu vi $110$ $m$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\left( x+\\dfrac{700}{x} \\right).2=110$. <br\/>Do \u0111\u00f3 \u0111\u00e1p \u00e1n A v\u00e0 C \u0111\u1ec1u \u0111\u00fang.<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n ch\u1ecdn l\u00e0 A v\u00e0 C <\/span><\/span>"}]}],"id_ques":983},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["140"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"Hai c\u1ea1nh c\u1ee7a m\u1ed9t m\u1ea3nh \u0111\u1ea5t h\u00ecnh ch\u1eef nh\u1eadt h\u01a1n k\u00e9m nhau $10$ $m.$ T\u00ednh chu vi m\u1ea3nh \u0111\u1ea5t \u1ea5y bi\u1ebft di\u1ec7n t\u00edch c\u1ee7a n\u00f3 b\u1eb1ng $1200$ $m^2$<br\/><b>\u0110\u00e1p s\u1ed1: <\/b> _input_ $(m)$","hint":"","explain":"<span class='basic_left'>G\u1ecdi chi\u1ec1u r\u1ed9ng c\u1ee7a m\u1ea3nh \u0111\u1ea5t l\u00e0 $x$ $(m),$ $x>0$<br\/>V\u00ec hai c\u1ea1nh c\u1ee7a m\u1ea3nh \u0111\u1ea5t h\u01a1n k\u00e9m nhau $10$ $m$ n\u00ean chi\u1ec1u d\u00e0i c\u1ee7a m\u1ea3nh \u0111\u1ea5t l\u00e0 $x+10$ $(m)$<br\/>Do di\u1ec7n t\u00edch c\u1ee7a n\u00f3 b\u1eb1ng $1200$ $m^2$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & x\\left( x+10 \\right)=1200 \\\\ & \\Leftrightarrow {{x}^{2}}+10x-1200=0 \\\\ & \\Delta '=1225\\Rightarrow \\sqrt{\\Delta '}=35 \\\\ & \\Rightarrow {{x}_{1}}=30;{{x}_{2}}=-40 \\\\ \\end{align}$ <br\/>V\u00ec $x>0$ n\u00ean $x=x_1=30$ <br\/>Suy ra m\u1ea3nh \u0111\u1ea5t c\u00f3 chi\u1ec1u r\u1ed9ng l\u00e0 $30$ $m$ v\u00e0 chi\u1ec1u d\u00e0i l\u00e0 $40$ $m$<br\/>Suy ra chu vi m\u1ea3nh \u0111\u1ea5t l\u00e0 $\\left( 30+40 \\right).2=140$ $(m)$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $140.$ <\/span><\/span>"}]}],"id_ques":984},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["12"],["5"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>T\u00ecm hai c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c vu\u00f4ng bi\u1ebft c\u1ea1nh huy\u1ec1n b\u1eb1ng $13$ $cm$ v\u00e0 t\u1ed5ng hai c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng $17$ $cm.$<br\/><b> \u0110\u00e1p s\u1ed1: <\/b>\u0110\u1ed9 d\u00e0i hai c\u1ea1nh g\u00f3c vu\u00f4ng l\u00e0 :_input_ $(cm)$ v\u00e0 _input_ $(cm)$<\/span>","hint":"","explain":"<span class='basic_left'>G\u1ecdi c\u1ea1nh th\u1ee9 nh\u1ea5t c\u1ee7a tam gi\u00e1c vu\u00f4ng c\u00f3 \u0111\u1ed9 d\u00e0i l\u00e0 $x$ $(cm).$ \u0110i\u1ec1u ki\u1ec7n: $ 0 < x < 17 $<br\/>V\u00ec t\u1ed5ng hai c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng $17$ $cm$ n\u00ean c\u1ea1nh c\u00f2n l\u1ea1i c\u1ee7a tam gi\u00e1c c\u00f3 \u0111\u1ed9 d\u00e0i l\u00e0 $17-x $ $(cm)$<br\/>Do c\u1ea1nh huy\u1ec1n b\u1eb1ng $13$ $cm$ n\u00ean \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pytago, ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,\\,{{x}^{2}}+{{\\left( 17-x \\right)}^{2}}={{13}^{2}} \\\\ & \\Leftrightarrow {{x}^{2}}+{{17}^{2}}-2.17x+{{x}^{2}}=169 \\\\ & \\Leftrightarrow 2{{x}^{2}}-34x+120=0 \\\\ & \\Leftrightarrow {{x}^{2}}-17x+60=0 \\\\ & \\Delta =49 \\\\ & \\Rightarrow {{x}_{1}}=\\dfrac{17+7}{2}=12 ;{{x}_{2}}=\\dfrac{17-7}{2}=5 \\,(\\text{th\u1ecfa m\u00e3n}) \\\\ \\end{align}$ <br\/>V\u00ec $x_1+x_2=12+5=17$ n\u00ean \u0111\u1ed9 d\u00e0i hai c\u1ea1nh g\u00f3c vu\u00f4ng l\u00e0 $12$ $cm$ v\u00e0 $5$ $cm$<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $12$ v\u00e0 $5.$ <\/span><\/span>"}]}],"id_ques":985},{"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 c\u1ea1nh c\u1ee7a m\u1ed9t \u0111a gi\u00e1c bi\u1ebft s\u1ed1 \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a \u0111a gi\u00e1c l\u00e0 $35.$","select":["A. $7$ c\u1ea1nh ","B. $8$ c\u1ea1nh","C. $9$ c\u1ea1nh ","D. $10$ c\u1ea1nh "],"hint":"\u0110a gi\u00e1c c\u00f3 $n$ c\u1ea1nh th\u00ec th\u00ec s\u1ed1 \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a \u0111a gi\u00e1c \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi c\u00f4ng th\u1ee9c: $\\dfrac{n\\left( n-3 \\right)}{2}$ ","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 c\u1ea1nh c\u1ee7a \u0111a gi\u00e1c l\u00e0 $n,$ $n \\in {{\\mathbb{N}}^{*}}$ <br\/>V\u00ec s\u1ed1 \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a \u0111a gi\u00e1c l\u00e0 $35$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/> $\\begin{align} & \\,\\,\\,\\,\\,\\,\\dfrac{n\\left( n-3 \\right)}{2}=35 \\\\ & \\Leftrightarrow {{n}^{2}}-3n=70 \\\\ & \\Leftrightarrow {{n}^{2}}-3n-70=0 \\\\ & \\Delta =289\\Rightarrow \\sqrt{\\Delta }=17 \\\\ & \\Rightarrow {{n}_{1}}=10;{{n}_{2}}=-7 \\\\ \\end{align}$ <br\/>V\u00ec $n \\in {{\\mathbb{N}}^{*}}$ n\u00ean $n=n_1=10$<br\/>V\u1eady \u0111a gi\u00e1c \u0111\u00e3 cho c\u00f3 $10$ c\u1ea1nh. <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span><\/span>","column":4}]}],"id_ques":986},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'>M\u1ed9t t\u1ed5 c\u00f4ng nh\u00e2n ph\u1ea3i l\u00e0m $144$ d\u1ee5ng c\u1ee5. Do $3$ c\u00f4ng nh\u00e2n chuy\u1ec3n \u0111i l\u00e0m vi\u1ec7c kh\u00e1c n\u00ean m\u1ed7i ng\u01b0\u1eddi c\u00f2n l\u1ea1i ph\u1ea3i l\u00e0m th\u00eam $4$ d\u1ee5ng c\u1ee5. T\u00ednh s\u1ed1 c\u00f4ng nh\u00e2n c\u1ee7a t\u1ed5 (coi n\u0103ng su\u1ea5t m\u1ed7i ng\u01b0\u1eddi l\u00e0 nh\u01b0 nhau). ","select":["A. 9 c\u00f4ng nh\u00e2n","B. 10 c\u00f4ng nh\u00e2n","C. 12 c\u00f4ng nh\u00e2n ","D. 21 c\u00f4ng nh\u00e2n"],"hint":"","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 c\u00f4ng nh\u00e2n c\u1ee7a t\u1ed5 l\u00e0 $x$ (ng\u01b0\u1eddi), $x\\in {{\\mathbb{N}}^{*}}$<br\/>V\u00ec ban \u0111\u1ea7u, t\u1ed5 c\u00f4ng nh\u00e2n ph\u1ea3i l\u00e0m $144$ d\u1ee5ng c\u1ee5 n\u00ean m\u1ed7i c\u00f4ng nh\u00e2n l\u00e0m $\\dfrac{144}{x}$ (d\u1ee5ng c\u1ee5)<br\/>Do $3$ c\u00f4ng nh\u00e2n chuy\u1ec3n \u0111i l\u00e0m vi\u1ec7c kh\u00e1c n\u00ean s\u1ed1 c\u00f4ng nh\u00e2n c\u00f2n l\u1ea1i l\u00e0 $x-3$ (ng\u01b0\u1eddi) v\u00e0 m\u1ed7i ng\u01b0\u1eddi ph\u1ea3i l\u00e0m $\\dfrac{144}{x-3}$ (d\u1ee5ng c\u1ee5). <br\/>V\u00ec m\u1ed7i ng\u01b0\u1eddi c\u00f2n l\u1ea1i ph\u1ea3i l\u00e0m th\u00eam $4$ d\u1ee5ng c\u1ee5 n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\dfrac{144}{x-3}-\\dfrac{144}{x}=4 \\\\ & \\Rightarrow 144x-144\\left( x-3 \\right)=4x\\left( x-3 \\right) \\\\ & \\Leftrightarrow 4{{x}^{2}}-12x-432=0 \\\\ & \\Leftrightarrow {{x}^{2}}-3x-108=0 \\\\ & \\Delta =441\\Rightarrow \\sqrt{\\Delta }=21 \\\\ & \\Rightarrow {{x}_{1}}=12;{{x}_{2}}=-9 \\\\ \\end{align}$<br\/>V\u00ec $x\\in {{\\mathbb{N}}^{*}}$ n\u00ean $x=x_1=12$<br\/>V\u1eady t\u1ed5 c\u00f4ng nh\u00e2n c\u00f3 $12$ ng\u01b0\u1eddi.<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":987},{"time":9,"part":[{"time":3,"title":"M\u1ed9t c\u00f4ng nh\u00e2n ph\u1ea3i l\u00e0m $420$ s\u1ea3n ph\u1ea9m. Do m\u1ed7i ng\u00e0y ng\u01b0\u1eddi \u0111\u00f3 t\u0103ng n\u0103ng su\u1ea5t $5$ s\u1ea3n ph\u1ea9m n\u00ean \u0111\u00e3 ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c s\u1edbm $7$ ng\u00e0y. T\u00ednh s\u1ed1 ng\u00e0y ng\u01b0\u1eddi \u0111\u00f3 l\u00e0m theo k\u1ebf ho\u1ea1ch.","title_trans":"H\u00e3y s\u1eafp x\u1ebfp c\u00e1c c\u00e2u sau \u0111\u1ec3 \u0111\u01b0\u1ee3c l\u1eddi gi\u1ea3i \u0111\u00fang","temp":"sequence","correct":[[[2],[6],[4],[1],[7],[5],[3]]],"list":[{"point":10,"image":"","left":["V\u00ec c\u00f4ng nh\u00e2n ph\u1ea3i l\u00e0m $420$ s\u1ea3n ph\u1ea9m n\u00ean m\u1ed7i ng\u00e0y ng\u01b0\u1eddi \u0111\u00f3 ph\u1ea3i l\u00e0m $\\dfrac{420}{x}$ (s\u1ea3n ph\u1ea9m).","Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, ta \u0111\u01b0\u1ee3c: ${{x}_{1}}=28;{{x}_{2}}=-21.$ V\u00ec $x>0$ n\u00ean $x=28$ ","V\u00ec ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c s\u1edbm $7$ ng\u00e0y n\u00ean th\u1eddi gian ng\u01b0\u1eddi c\u00f4ng nh\u00e2n \u0111\u00f3 l\u00e0m l\u00e0 $x-7$ (ng\u00e0y) v\u00e0 t\u01b0\u01a1ng \u1ee9ng m\u1ed7i ng\u00e0y l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{420}{x-7}$ (s\u1ea3n ph\u1ea9m) (2)","G\u1ecdi s\u1ed1 ng\u00e0y ng\u01b0\u1eddi c\u00f4ng nh\u00e2n l\u00e0m theo k\u1ebf ho\u1ea1ch l\u00e0 $x$ (ng\u00e0y), $x>0$","V\u1eady theo k\u1ebf ho\u1ea1ch th\u00ec c\u00f4ng nh\u00e2n \u0111\u00f3 ph\u1ea3i l\u00e0m trong $28$ ng\u00e0y.","T\u1eeb (1) v\u00e0 (2), ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{420}{x}+5=\\dfrac{420}{x-7}$","Th\u1ef1c t\u1ebf, m\u1ed7i ng\u00e0y ng\u01b0\u1eddi \u0111\u00f3 t\u0103ng n\u0103ng su\u1ea5t $5$ s\u1ea3n ph\u1ea9m, t\u1ee9c m\u1ed7i ng\u00e0y c\u00f4ng nh\u00e2n \u0111\u00f3 l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{420}{x}+5$ (s\u1ea3n ph\u1ea9m) (1)"],"top":90,"hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<\/span><br\/> <table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>S\u1ed1 s\u1ea3n ph\u1ea9m<br><\/th><th>S\u1ed1 ng\u00e0y<br><\/th><th>N\u0103ng su\u1ea5t (s\u1ea3n ph\u1ea9m\/ng\u00e0y)<br><\/th><\/tr><tr><th>K\u1ebf ho\u1ea1ch<br><\/th><td>$420$<\/td><td>$x$<\/td><td>$\\dfrac{420}{x}$<\/td><\/tr><tr><th>Th\u1ef1c t\u1ebf<br><\/th><td>$420$<\/td><td>$x-7$<\/td><td>$\\dfrac{420}{x-7}$ $\\left (= \\dfrac{420}{x}+5 \\right )$<\/td><\/tr><\/table><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi s\u1ed1 ng\u00e0y ng\u01b0\u1eddi c\u00f4ng nh\u00e2n l\u00e0m theo k\u1ebf ho\u1ea1ch l\u00e0 $x$ (ng\u00e0y), $x>0$<br\/>V\u00ec c\u00f4ng nh\u00e2n ph\u1ea3i l\u00e0m $420$ s\u1ea3n ph\u1ea9m n\u00ean m\u1ed7i ng\u00e0y ng\u01b0\u1eddi \u0111\u00f3 ph\u1ea3i l\u00e0m $\\dfrac{420}{x}$ (s\u1ea3n ph\u1ea9m).<br\/>Th\u1ef1c t\u1ebf, m\u1ed7i ng\u00e0y ng\u01b0\u1eddi \u0111\u00f3 t\u0103ng n\u0103ng su\u1ea5t $5$ s\u1ea3n ph\u1ea9m, t\u1ee9c m\u1ed7i ng\u00e0y c\u00f4ng nh\u00e2n \u0111\u00f3 l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{420}{x}+5$ (s\u1ea3n ph\u1ea9m) (1)<br\/>V\u00ec ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c s\u1edbm $7$ ng\u00e0y n\u00ean th\u1eddi gian ng\u01b0\u1eddi c\u00f4ng nh\u00e2n \u0111\u00f3 l\u00e0m l\u00e0 $x-7$ (ng\u00e0y) v\u00e0 t\u01b0\u01a1ng \u1ee9ng m\u1ed7i ng\u00e0y l\u00e0m \u0111\u01b0\u1ee3c $\\dfrac{420}{x-7}$ (s\u1ea3n ph\u1ea9m) (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\dfrac{420}{x}+5=\\dfrac{420}{x-7} \\\\ & \\Rightarrow 420\\left( x-7 \\right)+5x\\left( x-7 \\right)=420x \\\\ & \\Leftrightarrow 5{{x}^{2}}-35x-2940=0 \\\\ & \\Leftrightarrow {{x}^{2}}-7x-588=0 \\\\ & \\Delta =2401\\Rightarrow \\sqrt{\\Delta }=49 \\\\ & \\Rightarrow {{x}_{1}}=28;{{x}_{2}}=-21 \\\\ \\end{align}$ <br\/>V\u00ec $x>0$ n\u00ean $x=x_1=28$<br\/>V\u1eady theo k\u1ebf ho\u1ea1ch th\u00ec c\u00f4ng nh\u00e2n \u0111\u00f3 ph\u1ea3i l\u00e0m trong $28$ ng\u00e0y.<\/span>"}]}],"id_ques":988},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["80"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>M\u1ed9t t\u1ed5 s\u1ea3n xu\u1ea5t ph\u1ea3i l\u00e0m $800$ s\u1ea3n ph\u1ea9m theo k\u1ebf ho\u1ea1ch. T\u1ed5 \u0111\u00e3 t\u0103ng n\u0103ng su\u1ea5t $20$ s\u1ea3n ph\u1ea9m m\u1ed9t ng\u00e0y n\u00ean \u0111\u00e3 ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c tr\u01b0\u1edbc th\u1eddi h\u1ea1n $2$ ng\u00e0y. T\u00ednh s\u1ed1 s\u1ea3n ph\u1ea9m t\u1ed5 ph\u1ea3i l\u00e0m m\u1ed7i ng\u00e0y theo k\u1ebf ho\u1ea1ch.<br\/><b>\u0110\u00e1p s\u1ed1:<\/b> _input_ (s\u1ea3n ph\u1ea9m\/ng\u00e0y)<\/span>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<\/span><br\/> <table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>S\u1ed1 s\u1ea3n ph\u1ea9m<br><\/th><th>N\u0103ng su\u1ea5t (s\u1ea3n ph\u1ea9m\/ng\u00e0y)<br><\/th><th>S\u1ed1 ng\u00e0y<br><\/th><\/tr><tr><th>K\u1ebf ho\u1ea1ch<br><\/th><td>$800$<\/td><td>$x$<\/td><td>$\\dfrac{800}{x}$<\/td><\/tr><tr><th>Th\u1ef1c t\u1ebf<br><\/th><td>$800$<\/td><td>$x+20$<\/td><td>$\\dfrac{800}{x+20}$ $\\left (= \\dfrac{800}{x}-2 \\right )$<\/td><\/tr><\/table><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi s\u1ed1 s\u1ea3n ph\u1ea9m m\u00e0 t\u1ed5 ph\u1ea3i l\u00e0m m\u1ed7i ng\u00e0y theo k\u1ebf ho\u1ea1ch l\u00e0 $x$ (s\u1ea3n ph\u1ea9m), $x\\in {{\\mathbb{N}}^{*}}$ <br\/>Theo k\u1ebf ho\u1ea1ch th\u00ec t\u1ed5 s\u1ea3n xu\u1ea5t ph\u1ea3i l\u00e0m $800$ s\u1ea3n ph\u1ea9m n\u00ean th\u1eddi gian \u0111\u1ec3 t\u1ed5 ho\u00e0n th\u00e0nh l\u00e0 $\\dfrac{800}{x}$ (ng\u00e0y).<br\/>Th\u1ef1c t\u1ebf, t\u1ed5 \u0111\u00e3 t\u0103ng n\u0103ng su\u1ea5t $20$ s\u1ea3n ph\u1ea9m, t\u1ee9c m\u1ed7i ng\u00e0y c\u00f4ng nh\u00e2n \u0111\u00f3 l\u00e0m \u0111\u01b0\u1ee3c $x+20$ (s\u1ea3n ph\u1ea9m). Khi \u0111\u00f3 th\u1eddi gian \u0111\u1ec3 t\u1ed5 ho\u00e0n th\u00e0nh s\u1ea3n xu\u1ea5t l\u00e0 $\\dfrac{800}{x+20}$ (ng\u00e0y) (1)<br\/>V\u00ec ho\u00e0n th\u00e0nh c\u00f4ng vi\u1ec7c tr\u01b0\u1edbc th\u1eddi h\u1ea1n $2$ ng\u00e0y n\u00ean ta c\u0169ng c\u00f3 th\u1eddi gian \u0111\u1ec3 t\u1ed5 ho\u00e0n th\u00e0nh s\u1ea3n xu\u1ea5t l\u00e0 $\\dfrac{800}{x}-2$ (ng\u00e0y) (2)<br\/>T\u1eeb (1) v\u00e0 (2), ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\dfrac{800}{x+20}=\\dfrac{800}{x}-2 \\\\ & \\Rightarrow 800x=800\\left( x+20 \\right)-2x\\left( x+20 \\right) \\\\ & \\Leftrightarrow 2{{x}^{2}}+40x-16000=0 \\\\ & \\Leftrightarrow {{x}^{2}}+20x-8000=0 \\\\ & \\Delta '=8100\\Rightarrow \\sqrt{\\Delta' }=90 \\\\ & \\Rightarrow {{x}_{1}}=80;{{x}_{2}}=-100 \\\\ \\end{align}$<br\/> V\u00ec $x\\in {{\\mathbb{N}}^{*}}$ n\u00ean $x=x_1=80$<br\/>V\u1eady s\u1ed1 s\u1ea3n ph\u1ea9m t\u1ed5 ph\u1ea3i l\u00e0m m\u1ed7i ng\u00e0y theo k\u1ebf ho\u1ea1ch l\u00e0 $80$ s\u1ea3n ph\u1ea9m.<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $80.$ <\/span><\/span>"}]}],"id_ques":989},{"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\u1ed9t \u0111\u1ed9i th\u1ee7y l\u1ee3i g\u1ed3m $25$ ng\u01b0\u1eddi \u0111\u00e0o \u0111\u1eafp m\u1ed9t con m\u01b0\u01a1ng. \u0110\u1ed9i I \u0111\u00e0o $45$ $m^3$ \u0111\u1ea5t, \u0111\u1ed9i II \u0111\u00e0o $40$ $m^3$ \u0111\u1ea5t. Bi\u1ebft m\u1ed7i c\u00f4ng nh\u00e2n \u0111\u1ed9i II \u0111\u00e0o \u0111\u01b0\u1ee3c nhi\u1ec1u h\u01a1n m\u1ed7i c\u00f4ng nh\u00e2n \u0111\u1ed9i I l\u00e0 $1$ $m^3$ \u0111\u1ea5t. T\u00ednh s\u1ed1 \u0111\u1ea5t m\u1ed7i c\u00f4ng nh\u00e2n \u0111\u1ed9i I \u0111\u00e0o \u0111\u01b0\u1ee3c.","select":["A. $2$ $m^3$","B. $3$ $m^3$","C. $4$ $m^3$ ","D. $5$ $m^3$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<\/span><br\/> <table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>S\u1ed1 \u0111\u1ea5t \u0111\u00e0o \u0111\u01b0\u1ee3c $(m^3)$<br><\/th><th>S\u1ed1 \u0111\u1ea5t m\u1ed7i c\u00f4ng nh\u00e2n \u0111\u00e0o \u0111\u01b0\u1ee3c $(m^3)$<br><\/th><th>S\u1ed1 c\u00f4ng nh\u00e2n<br><\/th><\/tr><tr><th>\u0110\u1ed9i I<br><\/th><td>$45$<\/td><td>$x$<\/td><td>$\\dfrac{45}{x}$ <\/td><\/tr><tr><th>\u0110\u1ed9i II<br><\/th><td>$40$<\/td><td>$x+1$<\/td><td>$\\dfrac{40}{x+1}$ <\/td><\/tr><\/table><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi s\u1ed1 \u0111\u1ea5t m\u1ed7i c\u00f4ng nh\u00e2n \u0111\u1ed9i I \u0111\u00e0o \u0111\u01b0\u1ee3c l\u00e0 $x$ ($m^3$), $x>0$<br\/>V\u00ec m\u1ed7i c\u00f4ng nh\u00e2n \u0111\u1ed9i II \u0111\u00e0o \u0111\u01b0\u1ee3c nhi\u1ec1u h\u01a1n m\u1ed7i c\u00f4ng nh\u00e2n \u0111\u1ed9i I l\u00e0 $1$ $m^3$ \u0111\u1ea5t n\u00ean s\u1ed1 \u0111\u1ea5t m\u1ed7i c\u00f4ng nh\u00e2n \u0111\u1ed9i II \u0111\u00e0o \u0111\u01b0\u1ee3c l\u00e0 $x+1$ $(m^3)$<br\/>Do \u0111\u1ed9i I \u0111\u00e0o $45$ $m^3$ n\u00ean s\u1ed1 c\u00f4ng nh\u00e2n \u0111\u1ed9i I l\u00e0 $\\dfrac{45}{x}$ (ng\u01b0\u1eddi); \u0111\u1ed9i II \u0111\u00e0o $40$ $m^3$ n\u00ean s\u1ed1 c\u00f4ng nh\u00e2n \u0111\u1ed1i II l\u00e0 $\\dfrac{40}{x+1}$ (ng\u01b0\u1eddi)<br\/>Do \u0111\u1ed9i th\u1ee7y l\u1ee3i c\u00f3 $25$ ng\u01b0\u1eddi n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\dfrac{45}{x}+\\dfrac{40}{x+1}=25 \\\\ & \\Rightarrow 45\\left( x+1 \\right)+40x=25x\\left( x+1 \\right) \\\\ & \\Leftrightarrow 25{{x}^{2}}-60x-45=0 \\\\ & \\Leftrightarrow 5{{x}^{2}}-12x-9=0 \\\\ & \\Delta '=81 \\\\ & \\Rightarrow {{x}_{1}}=3;{{x}_{2}}=-0,6 \\\\ \\end{align}$ <br\/>V\u00ec $x>0$ n\u00ean $x =x_1=3$<br\/>V\u1eady m\u1ed7i c\u00f4ng nh\u00e2n \u0111\u1ed9i I \u0111\u00e0o \u0111\u01b0\u1ee3c l\u00e0 $3$ $m^3$ \u0111\u1ea5t.<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":4}]}],"id_ques":990}],"lesson":{"save":0,"level":1}}