{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" T\u00ecm $x, y$ bi\u1ebft:<br\/> $5x = 2y$ v\u00e0 $3x + 7y = - 82$ ","select":["A.$x = -4; y = -10$ ","B. $ x = -4; y = -8$ ","C. $x = 4; y = 10$","D. $x = -8; y = -20$"],"hint":" Ta c\u00f3: $5x = 2y \\Rightarrow \\dfrac{x}{2} = \\dfrac{y}{5} = \\dfrac{3x+7y}{3.2+7.5}$","explain":" Ta c\u00f3: $5x = 2y \\Rightarrow \\dfrac{x}{2} = \\dfrac{y}{5}$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta \u0111\u01b0\u1ee3c: <br\/> $ \\dfrac{x}{2} = \\dfrac{y}{5} = \\dfrac{3x+7y}{3.2+7.5} = \\dfrac{-82}{41} = -2$ <br\/> Suy ra: $ \\dfrac{x}{2} = -2 \\Rightarrow x = -4 \\\\ \\dfrac{y}{5} = -2 \\Rightarrow y = -10 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":2}]}],"id_ques":321},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"],["4"],["8"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm $x, y$ bi\u1ebft:<br\/> $\\dfrac{x}{3} = \\dfrac{y}{2} = \\dfrac{z}{4}$ v\u00e0 $x.y.z = 192$ <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_;$y =$ _input_","hint":" \u0110\u1eb7t : $\\dfrac{x}{3} = \\dfrac{y}{2} = \\dfrac{z}{4} = k $ r\u1ed3i bi\u1ec3u di\u1ec5n x, y, z theo k v\u00e0 th\u1ebf v\u00e0o gi\u1ea3 thi\u1ebft c\u00f2n l\u1ea1i","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> D\u1ea1ng to\u00e1n: T\u00ecm c\u00e1c s\u1ed1 h\u1ea1ng trong m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau bi\u1ebft t\u00edch c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u00f3 <\/b> <br\/> <i><u> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i <\/i> <\/u> <br\/> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c}$ v\u00e0 $x. y . z = p$ <br\/> Th\u00ec ta \u0111\u1eb7t $ \\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c} = k $ suy ra $\\begin{cases} x = ak \\\\ y = bk \\\\ z = ck \\end{cases} $ <br\/> T\u00ecm $k$ r\u1ed3i suy ra $x, y, z$. <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> \u0110\u1eb7t $\\dfrac{x}{3} = \\dfrac{y}{2} = \\dfrac{z}{4} = k \\\\ \\Rightarrow \\begin{cases} x = 3k \\\\ y = 2k \\\\ z = 4k \\end{cases} $ <br\/> Do \u0111\u00f3: $x.y.z = (3k).(2k).(4k) = 24k^{3}$ <br\/> Suy ra $24k^{3} = 192 \\Rightarrow k^{3} = \\dfrac{192}{24} = 8 \\Rightarrow k = 2 $ <br\/> Suy ra $\\dfrac{x}{3} = 2 \\Rightarrow x = 3.2 = 6 \\\\ \\dfrac{y}{2} = 2 \\Rightarrow y = 2.2 = 4 \\\\ \\dfrac{z}{4} = 2 \\Rightarrow z = 2.4 = 8 $ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c gi\u00e1 tr\u1ecb c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $6; 8; 4$ <\/span><\/span>"}]}],"id_ques":322},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["18"],["27"],["54"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $ 3x = 2y = z $ v\u00e0 $x + y + z = 99 ?$ <br\/><br\/> <b> \u0110\u00e1p s\u1ed1: <\/b>$x = $ _input_;$y =$ _input_; $z=$_input_","hint":" T\u1eeb: $3x = 2y = z $ ta chia cho BCNN(3; 2; 1) l\u00e0m xu\u1ea5t hi\u1ec7n d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> T\u00ednh ch\u1ea5t m\u1edf r\u1ed9ng c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau <\/b> <\/br> N\u1ebfu $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c}$ th\u00ec <br\/> $\\dfrac{x}{a} = \\dfrac{y}{b} = \\dfrac{z}{c} = \\dfrac{xm-yn+zt}{am-bn+ct}$<\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> T\u1eeb: $3x = 2y = z $ ta chia cho BCNN(3; 2; 1) = 6, ta \u0111\u01b0\u1ee3c: <br\/> $ \\dfrac{x}{2} = \\dfrac{y}{3} = \\dfrac{z}{6} $ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $\\dfrac{x}{2} = \\dfrac{y}{3} = \\dfrac{z}{6} = \\dfrac{x+y+z}{2+3+6} = \\dfrac{99}{11} = 9 $ <br\/> Suy ra $ \\dfrac{x}{2} = 9 \\Rightarrow x = 2.9 = 18 \\\\ \\dfrac{y}{3} = 9 \\Rightarrow y = 3.9 = 27 \\\\ \\dfrac{z}{6} = 9 \\Rightarrow z = 6.9 = 54 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady c\u00e1c gi\u00e1 tr\u1ecb c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $18; 27; 54$ <\/span><\/span>"}]}],"id_ques":323},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"],["-16"],["17"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $\\dfrac{x}{5} = \\dfrac{y}{-16} = \\dfrac{z}{17}$ v\u00e0 $3x - 2y = 47$ <br\/><br\/><b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_;$y =$ _input_; $z=$_input_","explain":" Ta c\u00f3: $\\dfrac{x}{5} = \\dfrac{y}{-16} = \\dfrac{z}{17}=\\dfrac{3x}{15} = \\dfrac{2y}{-32} $ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $ \\dfrac{3x}{15} = \\dfrac{2y}{-32} = \\dfrac{3x-2y}{15-(-32)} = \\dfrac{47}{47} = 1 $ <br\/> Suy ra $ \\dfrac{x}{5} = 1 \\Rightarrow x = 5.1 = 5 \\\\ \\dfrac{y}{-16} = 1 \\Rightarrow y = -16.1 = -16 \\\\ \\dfrac{z}{17} = 1 \\Rightarrow z = 17.1 = 17 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady c\u00e1c gi\u00e1 tr\u1ecb c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $5;-16;17$<\/span>"}]}],"id_ques":324},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["28"],["12"],["16"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $\\dfrac{x}{7} = \\dfrac{y}{3} = \\dfrac{z}{4}$ v\u00e0 $y + z = 28 $ <br\/><br\/> <b> \u0110\u00e1p s\u1ed1: <\/b>$x = $ _input_;$y =$ _input_; $z=$_input_","explain":"Ta c\u00f3: $\\dfrac{x}{7} = \\dfrac{y}{3} = \\dfrac{z}{4}$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $ \\dfrac{y}{3} = \\dfrac{z}{4} = \\dfrac{y+z}{3+4} = \\dfrac{28}{7} = 4 $ <br\/> Suy ra $ \\dfrac{x}{7} = 4 \\Rightarrow x = 7.4 = 28 \\\\ \\dfrac{y}{3} = 4 \\Rightarrow y = 3.4 = 12 \\\\ \\dfrac{z}{4} = 4 \\Rightarrow z = 4.4 = 16 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady c\u00e1c gi\u00e1 tr\u1ecb c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $28; 12; 16$<\/span><\/span>"}]}],"id_ques":325},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"],["6"],["12"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $\\dfrac{x}{2} = \\dfrac{y}{3} = \\dfrac{z}{6}$ v\u00e0 $3x - 2y + 2z = 24 $ <br\/><br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_;$y =$ _input_; $z=$_input_","explain":" Ta c\u00f3: $ \\dfrac{x}{2} = \\dfrac{y}{3} = \\dfrac{z}{6} = \\dfrac{3x}{6} = \\dfrac{2y}{6} = \\dfrac{2z}{12}$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $ \\dfrac{3x}{6} = \\dfrac{2y}{6} = \\dfrac{2z}{12} = \\dfrac{3x-2y+2z}{6-6+12} = \\dfrac{24}{12} = 2 $ <br\/> Suy ra $ \\dfrac{x}{2} = 2 \\Rightarrow x = 2.2 = 4 \\\\ \\dfrac{y}{3} = 2 \\Rightarrow y = 3.2 = 6 \\\\ \\dfrac{z}{6} = 2 \\Rightarrow z = 6.2 = 12 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady c\u00e1c gi\u00e1 tr\u1ecb c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $4;6;12$<\/span>"}]}],"id_ques":326},{"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":" T\u00ecm $x, y$ bi\u1ebft: <br\/> $4x = -5y$ v\u00e0 $x.y = -80 $ ","select":["A.$x = -10; y = 8$ ho\u1eb7c $x = -10; y = -8$ ","B. $ x = 10; y = -8$ ho\u1eb7c $x = -10; y = 8$","C. $x = 10; y = -8$","D. $x = -10; y = 8$"],"hint":" \u0110\u01b0a v\u1ec1 d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau v\u00e0 bi\u1ec3u di\u1ec5n x, y theo k","explain":" Ta c\u00f3: $4x = -5y \\Rightarrow \\dfrac{x}{-5} = \\dfrac{y}{4} $ <br\/> Ta \u0111\u1eb7t $\\dfrac{x}{-5} = \\dfrac{y}{4} = k $ <br\/> Suy ra: $\\begin{cases} x = -5k \\\\ y = 4k \\end{cases} $ <br\/> Do \u0111\u00f3: $x.y = (-5k).(4k) = -20k^{2}$ <br\/> V\u1eady $-20k^{2} = -80 \\Rightarrow k^{2} = 4 \\Rightarrow k = \\pm 2 $ <br\/> N\u1ebfu $k = 2 \\Rightarrow \\begin{cases} x = -5.2 = -10 \\\\ y = 4.2 = 8 \\end{cases} $ <br\/> N\u1ebfu $k = -2 \\Rightarrow \\begin{cases} x = (-5).(-2) = 10 \\\\ y = 4.(-2) = -8 \\end{cases} $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = -10 \\\\ y = 8 \\end{cases}$ ho\u1eb7c $ \\begin{cases} x = 10 \\\\ y = -8 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":327},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["6"],["8"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ecm hai s\u1ed1 $x, y$ d\u01b0\u01a1ng bi\u1ebft r\u1eb1ng: <br\/> $4x = 3y$ v\u00e0 $x^{2} + y^{2} = 100 $ <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b>$x = $ _input_;$y =$ _input_","explain":" T\u1eeb $ 4x = 3y \\Rightarrow \\dfrac{x}{3} = \\dfrac{y}{4} \\Rightarrow \\left(\\dfrac{x}{3}\\right)^{2} = \\left(\\dfrac{y}{4}\\right)^{2} $ (b\u00ecnh ph\u01b0\u01a1ng hai v\u1ebf) <br\/> $ \\Rightarrow \\dfrac{x^{2}}{9} = \\dfrac{y^{2}}{16}$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $ \\dfrac{x^{2}}{9} = \\dfrac{y^{2}}{16} = \\dfrac{x^{2}+y^{2}}{9+16} = \\dfrac{100}{25} = 4 $ <br\/> Suy ra: $ x^{2} = 9.4 = 36 \\Rightarrow x = \\pm 6 \\\\ y^{2} = 16.4 = 64 \\Rightarrow y = \\pm 8 $ <br\/> M\u00e0 $x, y$ l\u00e0 s\u1ed1 d\u01b0\u01a1ng n\u00ean $x=6; y=8$ th\u1ecfa m\u00e3n \u0111\u1ec1 b\u00e0i <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 6 v\u00e0 8 <\/span><\/span>"}]}],"id_ques":328},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"],["4"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ecm hai s\u1ed1 $x, y$ bi\u1ebft r\u1eb1ng: <br\/> $\\dfrac{x}{5} = \\dfrac{y}{4}$ v\u00e0 $x^{2}.y = 100 $ <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b>$x = $ _input_;$y =$ _input_","explain":" \u0110\u1eb7t $ \\dfrac{x}{5} = \\dfrac{y}{4} = k \\Rightarrow \\begin{cases} x = 5k \\\\ y = 4k \\end{cases} $ <br\/> Do \u0111\u00f3: $x^{2}.y = (5k)^{2}.(4k) = 100k^{3}$ <br\/> $\\Rightarrow 100k^{3} = 100 \\Rightarrow k^{3} = 1 \\Rightarrow k = 1 $ <br\/> Suy ra: $\\dfrac{x}{5} = 1 \\Rightarrow x = 5.1=5 \\\\ \\dfrac{y}{4} = 1 \\Rightarrow y = 1.4 = 4 $ <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0 5 v\u00e0 4 <\/span><\/span>"}]}],"id_ques":329},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"],["3"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ecm hai s\u1ed1 $x, y$ d\u01b0\u01a1ng bi\u1ebft r\u1eb1ng: <br\/> $\\dfrac{x}{5} = \\dfrac{y}{3}$ v\u00e0 $x^{2} - y^{2} = 16? $ <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b>$x = $ _input_;$y =$ _input_","hint":" Quan s\u00e1t gi\u1ea3 thi\u1ebft 2 c\u00f3 hi\u1ec7u b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a x v\u00e0 y n\u00ean ta b\u00ecnh ph\u01b0\u01a1ng 2 v\u1ebf c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c v\u00e0 \u00e1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ","explain":" T\u1eeb $ \\dfrac{x}{5} = \\dfrac{y}{3} \\Rightarrow \\left(\\dfrac{x}{5}\\right)^{2} = \\left(\\dfrac{y}{3}\\right)^{2} $ (b\u00ecnh ph\u01b0\u01a1ng hai v\u1ebf) <br\/> $ \\Rightarrow \\dfrac{x^{2}}{25} = \\dfrac{y^{2}}{9}$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $ \\dfrac{x^{2}}{25} = \\dfrac{y^{2}}{9} = \\dfrac{x^{2}-y^{2}}{25-9} = \\dfrac{16}{16} = 1 $ <br\/> Suy ra: $ x^{2} = 25.1 = 25 \\Rightarrow x = \\pm 5 \\\\ y^{2} = 9.1 = 9 \\Rightarrow y = \\pm 3 $ <br\/> M\u00e0 $x, y$ l\u00e0 s\u1ed1 d\u01b0\u01a1ng n\u00ean $x =5; y=3$ th\u1ecfa m\u00e3n \u0111\u1ec1 b\u00e0i <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 5 v\u00e0 3 <\/span><\/span>"}]}],"id_ques":330},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-5"],["2"],["2"],["-3"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $\\dfrac{x}{5} = \\dfrac{y}{-4} = \\dfrac{z}{6}$ v\u00e0 $x.y.z = 15?$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>;$y =$ _input_; $z=$_input_$","explain":" \u0110\u1eb7t $\\dfrac{x}{5} = \\dfrac{y}{-4} = \\dfrac{z}{6} = k \\\\ \\Rightarrow \\begin{cases} x = 5k \\\\ y = -4k \\\\ z = 6k \\end{cases} $ <br\/> Do \u0111\u00f3: $x.y.z = (5k).(-4k).(6k) = -120k^{3}$ <br\/> Suy ra $-120k^{3} = 15 \\Rightarrow k^{3} = \\dfrac{15}{-120} = \\dfrac{-1}{8} = \\left(\\dfrac{-1}{2}\\right)^{3} \\\\ \\Rightarrow k = \\dfrac{-1}{2}$ <br\/> <br\/> <span class='basic_pink'>Suy ra $ \\dfrac{x}{5} = \\dfrac{-1}{2} \\Rightarrow x = \\dfrac{-5}{2} \\\\ \\dfrac{y}{-4} = \\dfrac{-1}{2} \\Rightarrow y = 2 \\\\ \\dfrac{z}{6} = \\dfrac{-1}{2} \\Rightarrow z = -3 $ <br\/><\/span><\/span>"}]}],"id_ques":331},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["18"],["27"],["36"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" Chu vi c\u1ee7a m\u1ed9t tam gi\u00e1c l\u00e0 $81$ cm. C\u00e1c c\u1ea1nh c\u1ee7a n\u00f3 t\u1ec9 l\u1ec7 v\u1edbi $2, 3, 4$. T\u00ednh \u0111\u1ed9 d\u00e0i m\u1ed7i c\u1ea1nh <br\/><br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> \u0110\u1ed9 d\u00e0i ba c\u1ea1nh c\u1ee7a tam gi\u00e1c l\u1ea7n l\u01b0\u1ee3t l\u00e0: (_input_ cm; _input _cm; _input_ cm )","hint":"\u0110\u1eb7t \u1ea9n cho c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c v\u00e0 bi\u1ec3u di\u1ec5n theo c\u00e1c d\u1eef ki\u1ec7n c\u1ee7a \u0111\u1ec1 b\u00e0i ","explain":" G\u1ecdi \u0111\u1ed9 d\u00e0i ba c\u1ea1nh c\u1ee7a tam gi\u00e1c l\u1ea7n l\u01b0\u1ee3t l\u00e0 $x, y, z (x; y; z > 0)$. <br\/> Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3: $\\dfrac{x}{2} = \\dfrac{y}{3} = \\dfrac{z}{4}$ v\u00e0 $x + y + z = 81$ <br\/> Theo t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau: <br\/> $\\dfrac{x}{2} = \\dfrac{y}{3} = \\dfrac{z}{4} = \\dfrac{x+y+z}{2+3+4} = \\dfrac{81}{9} = 9$ <br\/> Suy ra $\\dfrac{x}{2} = 9 \\Rightarrow x = 18 \\\\ \\dfrac{y}{3} = 9 \\Rightarrow y = 27 \\\\ \\dfrac{z}{4} = 9 \\Rightarrow z = 36$<br\/> <br\/> <span class='basic_pink'> V\u1eady \u0111\u1ed9 d\u00e0i ba c\u1ea1nh c\u1ee7a tam gi\u00e1c l\u1ea7n l\u01b0\u1ee3t l\u00e0 $18$ cm; $27$ cm; $36$ cm <\/span><\/span>"}]}],"id_ques":332},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["20"],["12"],["42"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $\\dfrac{x}{10} = \\dfrac{y}{6} = \\dfrac{z}{21}$ v\u00e0 $5x + y - 2z = 28?$ <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b>$x = $ _input_;$y =$ _input_; $z=$_input_","explain":" Ta c\u00f3: $ \\dfrac{x}{10} = \\dfrac{y}{6} = \\dfrac{z}{21} \\Rightarrow \\dfrac{5x}{50} = \\dfrac{y}{6} = \\dfrac{2z}{42}$ <br\/> Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{5x}{50} = \\dfrac{y}{6} = \\dfrac{2z}{42} = \\dfrac{5x+y-2z}{50+6-42}= \\dfrac{28}{14} = 2 $ <br\/> Suy ra: $\\dfrac{x}{10} = 2 \\Rightarrow x = 10.2 = 20 \\\\ \\dfrac{y}{6} = 2 \\Rightarrow y = 6.2 = 12 \\\\ \\dfrac{z}{21} = 2 \\Rightarrow z = 21.2 = 42 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x, y, z$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 $20; 12; 42$<\/span> "}]}],"id_ques":333},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["70"],["60"],["96"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm c\u00e1c s\u1ed1 a, b, c bi\u1ebft: <br\/> $a - 2b + c = 46 $ v\u00e0 $ \\dfrac{a}{7} = \\dfrac{b}{6}, \\dfrac{b}{5} = \\dfrac{c}{8}?$ <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b>$a = $ _input_;$b =$ _input_; $c=$_input_","hint":" L\u00e0m xu\u1ea5t hi\u1ec7n d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, b\u1eb1ng c\u00e1ch \u0111\u01b0a m\u1eabu s\u1ed1 c\u1ee7a b \u1edf 2 t\u1ec9 l\u1ec7 th\u1ee9c $ \\dfrac{a}{7} = \\dfrac{b}{6}, \\dfrac{b}{5} = \\dfrac{c}{8}?$ v\u1ec1 gi\u1ed1ng nhau ","explain":" Ta c\u00f3: $ \\dfrac{a}{7} = \\dfrac{b}{6} \\Rightarrow \\dfrac{a}{35} = \\dfrac{b}{30} (1) \\\\ \\dfrac{b}{5} = \\dfrac{c}{8} \\Rightarrow \\dfrac{b}{30} = \\dfrac{c}{48} (2)$ <br\/> T\u1eeb (1) v\u00e0 (2) suy ra $\\dfrac{a}{35} = \\dfrac{b}{30} = \\dfrac{c}{48} = \\dfrac{2b}{60} $ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $\\dfrac{a}{35} = \\dfrac{2b}{60} = \\dfrac{c}{48} = \\dfrac{a-2b+c}{35-60+48} = \\dfrac{46}{23} = 2 $ <br\/> Do \u0111\u00f3: $\\dfrac{a}{35} = 2 \\Rightarrow a = 35.2 = 70 \\\\ \\dfrac{b}{30} = 2 \\Rightarrow b = 30.2 = 60 \\\\ \\dfrac{c}{48} = 2 \\Rightarrow c = 48.2 = 96 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $a, b, c$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 $70; 60; 96$ <\/span><\/span> "}]}],"id_ques":334},{"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":" T\u00ecm $x$ bi\u1ebft: <br\/> $ (15 + x) : (7 + x) = 4 : 3 $ ","select":["A. $8$ ","B. $ 7$ ","C. $17$","D. $1$"],"explain":" Ta c\u00f3: $ (15 + x) : (7 + x) = 4 : 3$ <br\/> Suy ra: $ \\dfrac{15+x}{4} = \\dfrac{7+x}{3} $ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $ \\dfrac{15+x}{4} = \\dfrac{7+x}{3} = \\dfrac{(15 + x)-(7 + x)}{4-3} \\\\ = \\dfrac{15+x-7-x}{4-3} \\\\ = \\dfrac{8}{1} = 8 $ <br\/> Suy ra: $\\dfrac{15+x}{4} = 8 \\\\ \\Rightarrow 15 + x = 4.8 = 32 \\\\ \\Rightarrow x = 32 - 15 = 17 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x $ l\u00e0: $17$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":335},{"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":" T\u00ecm $x$ bi\u1ebft: <br\/> $ (x + 15) : x = 4 : 3 $ ","select":["A. $5$ ","B. $ 45$ ","C. $60$","D. $75$"],"explain":" Ta c\u00f3: $ (x + 15) : x = 4 : 3 $ <br\/> Suy ra: $ \\dfrac{x+15}{4} = \\dfrac{x}{3} $ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $ \\dfrac{x+15}{4} = \\dfrac{x}{3} = \\dfrac{(x+15)-x}{4-3} \\\\ = \\dfrac{x+15-x}{4-3} = \\dfrac{15}{1} = 15$ <br\/> Suy ra: $\\dfrac{x}{3} = 15 \\Rightarrow x = 3.15 = 45 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x $ l\u00e0: $45$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":336},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $\\dfrac{x}{20} = \\dfrac{y}{9} = \\dfrac{z}{6}$ v\u00e0 $x - 2y + 4z = 13? $ ","select":["A.$x = 10; y = 4,5; z = 3$ ","B. $ x = 40; y = 18; z = 12$ ","C. $x = 4; y = 3; z = 2$"],"explain":" Ta c\u00f3 $ \\dfrac{x}{20} = \\dfrac{y}{9} = \\dfrac{z}{6} \\Leftrightarrow \\dfrac{x}{20} = \\dfrac{2y}{18} = \\dfrac{4z}{24} $ <br\/> Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $\\dfrac{x}{20} = \\dfrac{2y}{18} = \\dfrac{4z}{24} = \\dfrac{x-2y+4z}{20-18+24}= \\dfrac{13}{26} = \\dfrac{1}{2} $ <br\/> Suy ra: $\\dfrac{x}{20} = \\dfrac{1}{2} \\Rightarrow x = \\dfrac{20.1}{2} = 10 \\\\ \\dfrac{y}{9} = \\dfrac{1}{2} \\Rightarrow y = \\dfrac{1.9}{2} = 4,5 \\\\ \\dfrac{z}{6} = \\dfrac{1}{2} \\Rightarrow z = \\dfrac{6.1}{2} = 3 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x, y, z$ l\u00e0: $\\begin{cases} x = 10 \\\\ y = 4,5 \\\\ z = 3 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":1}]}],"id_ques":337},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["195"],["105"],["75"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $\\dfrac{x}{13} = \\dfrac{y}{7} = \\dfrac{z}{5}$ v\u00e0 $x - y - 2z = -60?$ <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b>$x = $ _input_;$y =$ _input_; $z=$_input_","explain":" Ta c\u00f3: $ \\dfrac{x}{13} = \\dfrac{y}{7} = \\dfrac{z}{5} \\Rightarrow \\dfrac{x}{13} = \\dfrac{y}{7} = \\dfrac{2z}{10}$ <br\/> Theo t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta c\u00f3: <br\/> $ \\dfrac{x}{13} = \\dfrac{y}{7} = \\dfrac{2z}{10} = \\dfrac{x-y-2z}{13-7-10}= \\dfrac{-60}{-4} = 15 $ <br\/> Suy ra: $\\dfrac{x}{13} = 15 \\Rightarrow x = 13.15 = 195 \\\\ \\dfrac{y}{7} = 15 \\Rightarrow y = 7.15 = 105 \\\\ \\dfrac{z}{5} = 15 \\Rightarrow z = 5.15 = 75 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x, y, z$ l\u1ea7n l\u01b0\u1ee3t l\u00e0 $195; 105; 75$ <\/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":" T\u00ecm $x, y$ bi\u1ebft: <br\/> $x : y = 2 : 3$ v\u00e0 $x.y = 54 (x, y \\neq 0)$ ","select":["A.$x = 8; y = 12$ ho\u1eb7c $x = -8; y = -12$ ","B. $ x = 6; y = 9$ ho\u1eb7c $x = -6; y = -9$","C. $x = 12; y = 18$","D. $x = -12; y = -18$"],"hint":"\u0110\u01b0a v\u1ec1 t\u1ec9 l\u1ec7 th\u1ee9c v\u00e0 bi\u1ec3u di\u1ec5n x, y theo k ","explain":" Ta c\u00f3 $x : 2 = 3 : y \\Leftrightarrow \\dfrac{x}{2} = \\dfrac{3}{y}$ <br\/> Ta \u0111\u1eb7t $\\dfrac{x}{2} = \\dfrac{y}{3} = k $ <br\/> Suy ra: $\\begin{cases} x = 2k \\\\ y = 3k \\end{cases} $ <br\/> Do \u0111\u00f3: $x.y = (2k).(3k) = 6k^{2}$ <br\/> V\u1eady $6k^{2} = 54 \\Rightarrow k^{2} = 9 \\Rightarrow k = \\pm 3 $ <br\/> N\u1ebfu $k = 3 \\Rightarrow \\begin{cases} x = 2.3 = 6 \\\\ y = 3.3 = 9 \\end{cases} $ <br\/> N\u1ebfu $k = -3 \\Rightarrow \\begin{cases} x = 2.(-3) = -6 \\\\ y = 3.(-3) = -9 \\end{cases} $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 6 \\\\ y = 9 \\end{cases}$ ho\u1eb7c $ \\begin{cases} x = -6 \\\\ y = -9 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":339},{"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":" T\u00ecm $x, y$ bi\u1ebft: <br\/> $\\dfrac{x}{5} = \\dfrac{y}{2}$ v\u00e0 $x.y = 1000$ ","select":["A.$x = -50; y = 20$ ho\u1eb7c $x = -50; y = -20$ ","B. $ x = 50; y = 20$ ho\u1eb7c $x = -50; y = -20$","C. $x = 50; y = 20$","D. $x = -50; y = -20$"],"explain":" Ta \u0111\u1eb7t $\\dfrac{x}{5} = \\dfrac{y}{2} = k $ <br\/> Suy ra: $\\begin{cases} x = 5k \\\\ y = 2k \\end{cases} $ <br\/> Do \u0111\u00f3: $x.y = (5k).(2k) = 10k^{2}$ <br\/> V\u1eady $10k^{2} = 1000 \\Rightarrow k^{2} = 100 \\Rightarrow k = \\pm 10 $ <br\/> N\u1ebfu $k = 10 \\Rightarrow \\begin{cases} x = 5.10 = 50 \\\\ y = 2.10 = 20 \\end{cases} $ <br\/> N\u1ebfu $k = -10 \\Rightarrow \\begin{cases} x = 5.(-10) = -50 \\\\ y = 2.(-10) = -20 \\end{cases} $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ v\u00e0 $y$ l\u00e0: $\\begin{cases} x = 50 \\\\ y = 20 \\end{cases}$ ho\u1eb7c $ \\begin{cases} x = -50 \\\\ y = -20 \\end{cases}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":340}],"lesson":{"save":0,"level":2}}