{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p s\u1ed1 \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["80"],["120"],["192"]]],"list":[{"point":10,"width":80,"type_input":"","ques":" T\u00ecm a, b, c bi\u1ebft: <br\/> $5a - 3b - 3c = -536 $ v\u00e0 $\\dfrac{a}{4} = \\dfrac{b}{6}, \\dfrac{b}{5} = \\dfrac{c}{8} $ <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1:<\/b>$a = $ _input_;$b =$ _input_; $c=$_input_","hint":"Ta n\u1ed1i hai t\u1ec9 l\u1ec7 th\u1ee9c th\u00e0nh m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau b\u1edfi m\u1eaft x\u00edch l\u00e0 $b$ nh\u01b0 sau: Chia hai v\u1ebf c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c th\u1ee9 nh\u1ea5t cho 5 v\u00e0 chia hai v\u1ebf c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c th\u1ee9 2 cho $6.$","explain":" Ta n\u1ed1i hai t\u1ec9 l\u1ec7 th\u1ee9c: $\\dfrac{a}{4} = \\dfrac{b}{6}$ v\u00e0 $ \\dfrac{b}{5} = \\dfrac{c}{8} $ th\u00e0nh m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau b\u1edfi m\u1eaft x\u00edch l\u00e0 $b$ nh\u01b0 sau: <br\/> Chia hai v\u1ebf c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c th\u1ee9 nh\u1ea5t cho $5,$ ta \u0111\u01b0\u1ee3c: $\\dfrac{a}{20} = \\dfrac{b}{30}$ <br\/> Chia hai v\u1ebf c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c th\u1ee9 2 cho $6,$ ta \u0111\u01b0\u1ee3c: $\\dfrac{b}{30} = \\dfrac{c}{48}$ <br\/> T\u1eeb \u0111\u00f3: $\\dfrac{a}{20} = \\dfrac{b}{30} = \\dfrac{c}{48}$ $\\Rightarrow \\dfrac{5a}{100} = \\dfrac{3b}{90} = \\dfrac{3c}{144}$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $\\dfrac{5a}{100} = \\dfrac{3b}{90} = \\dfrac{3c}{144} = \\dfrac{5a-3b-3c}{100-90-144} = \\dfrac{-536}{-134} = 4 $<br\/> Suy ra: $\\dfrac{a}{20} = 4 \\Rightarrow a = 80 \\\\ \\dfrac{b}{30} = 4 \\Rightarrow b = 120 \\\\ \\dfrac{c}{48} = 4 \\Rightarrow c = 192 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $a, b, c$ l\u00e0: $\\begin{cases} a = 80 \\\\ b = 120 \\\\ c = 192 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":341},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p s\u1ed1 \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["63"],["105"],["36"]]],"list":[{"point":10,"width":70,"type_input":"","ques":" <span class='basic_left'> T\u00ecm ba s\u1ed1 nguy\u00ean, bi\u1ebft r\u1eb1ng BCNN c\u1ee7a ch\u00fang b\u1eb1ng $1260.$ T\u1ec9 s\u1ed1 c\u1ee7a s\u1ed1 th\u1ee9 nh\u1ea5t v\u00e0 s\u1ed1 th\u1ee9 hai l\u00e0 $3:5.$ T\u1ec9 s\u1ed1 c\u1ee7a s\u1ed1 th\u1ee9 ba v\u00e0 s\u1ed1 th\u1ee9 nh\u1ea5t l\u00e0 $4:7 $ <\/span> <br\/> <br\/> <u>\u0110\u00e1p s\u1ed1: <\/u> Ba s\u1ed1 l\u1ea7n l\u01b0\u1ee3t l\u00e0: (_input_;_input_;_input_)","hint":" \u0110\u1eb7t \u1ea9n r\u1ed3i \u0111\u01b0a v\u1ec1 c\u00e1c t\u1ec9 l\u1ec7 th\u1ee9c v\u00e0 l\u00e0m xu\u1ea5t hi\u1ec7n d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau","explain":" G\u1ecdi ba s\u1ed1 l\u1ea7n l\u01b0\u1ee3t l\u00e0 $x, y, z$. Theo gi\u1ea3 thi\u1ebft, ta c\u00f3: <br\/> $\\dfrac{x}{y} = \\dfrac{3}{5}; \\dfrac{z}{x} = \\dfrac{4}{7} \\Rightarrow \\dfrac{x}{3} = \\dfrac{y}{5}; \\dfrac{z}{4} = \\dfrac{x}{7}$ <br\/> Ta c\u00f3:$\\dfrac{x}{3} = \\dfrac{y}{5} \\Rightarrow \\dfrac{x}{21} = \\dfrac{y}{35} \\\\ \\dfrac{z}{4} = \\dfrac{x}{7} \\Rightarrow \\dfrac{z}{12} = \\dfrac{x}{21} \\\\ \\Rightarrow \\dfrac{x}{21} = \\dfrac{y}{35} = \\dfrac{z}{12} $ <br\/> \u0110\u1eb7t: $ \\dfrac{x}{21} = \\dfrac{y}{35} = \\dfrac{z}{12} = k \\Rightarrow \\begin{cases} x = 21k \\\\ y = 35k \\\\ z = 12k \\end{cases}$ <br\/> C\u00f3: BCNN $ (x; y; z) = (21k; 35k; 12k) = (21; 35; 12)k = 420k$ <br\/> Suy ra: $420k = 1260 \\Rightarrow k = 3$ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a x, y, z l\u00e0 : $ \\begin{cases} x = 21.3 = 63 \\\\ y = 35.3 = 105 \\\\ z = 12.3 = 36 \\end{cases}$ <\/span><\/span>"}]}],"id_ques":342},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p s\u1ed1 \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-84"],["63"],["54"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" T\u00ecm $x, y, z$ bi\u1ebft: <br\/> $-3x = 4y; 6y = 7z $ v\u00e0 $x - 2y + 3z = -48$ <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1:<\/b>$x = $ _input_;$y =$ _input_; $z=$_input_","hint":"","explain":" T\u1eeb $ -3x = 4y; 6y = 7z \\Rightarrow \\dfrac{x}{4} = \\dfrac{y}{-3}; \\dfrac{y}{7} = \\dfrac{z}{6}$ <br\/> Ta n\u1ed1i hai t\u1ec9 l\u1ec7 th\u1ee9c: $\\dfrac{x}{4} = \\dfrac{y}{-3}$ v\u00e0 $ \\dfrac{y}{7} = \\dfrac{z}{6} $ th\u00e0nh m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau b\u1edfi m\u1eaft x\u00edch l\u00e0 $y$ nh\u01b0 sau: <br\/> Chia hai v\u1ebf c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c th\u1ee9 nh\u1ea5t cho $-7,$ ta \u0111\u01b0\u1ee3c: $\\dfrac{x}{-28} = \\dfrac{y}{21}$ <br\/> Chia hai v\u1ebf c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c th\u1ee9 2 cho $3,$ ta \u0111\u01b0\u1ee3c: $ \\dfrac{y}{21} = \\dfrac{z}{18}$ <br\/> T\u1eeb \u0111\u00f3: $\\dfrac{x}{-28} = \\dfrac{y}{21} = \\dfrac{z}{18}$ $\\Rightarrow \\dfrac{x}{-28} = \\dfrac{2y}{42} = \\dfrac{3z}{54}$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $\\dfrac{x}{-28} = \\dfrac{2y}{42} = \\dfrac{3z}{54} = \\dfrac{x-2y+3z}{-28-42+54} = \\dfrac{-48}{-16} = 3 $<br\/> Suy ra: $\\dfrac{x}{-28} = 3 \\Rightarrow x = -84 \\\\ \\dfrac{y}{21} = 3 \\Rightarrow y = 63 \\\\ \\dfrac{z}{18} = 3 \\Rightarrow z = 54 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x, y, z$ l\u00e0: $\\begin{cases} x = -84 \\\\ y = 63 \\\\ z = 54 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":343},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p s\u1ed1 \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["9"],["16"],["29"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" <span class='basic_left'> L\u1edbp 7A c\u00f3 54 h\u1ecdc sinh \u0111\u01b0\u1ee3c chia l\u00e0m 3 t\u1ed5. N\u1ebfu t\u1ed5 1 th\u00eam v\u00e0o 3 h\u1ecdc sinh, t\u1ed5 2 th\u00eam 2 h\u1ecdc sinh, t\u1ed5 3 b\u1edbt \u0111i 5 h\u1ecdc sinh th\u00ec s\u1ed1 h\u1ecdc sinh t\u1ed5 1, 2, 3 t\u1ec9 l\u1ec7 v\u1edbi 2, 3, 4. <br\/> T\u00ecm s\u1ed1 h\u1ecdc sinh m\u1ed7i t\u1ed5 . <\/span> <br\/> T\u1ed5 1 = _input_ (h\u1ecdc sinh) <br\/> T\u1ed5 2 = $_input_(h\u1ecdc sinh) <br\/> T\u1ed5 3 = _input_(h\u1ecdc sinh)","hint":" \u0110\u1eb7t \u1ea9n v\u00e0 bi\u1ec3u di\u1ec5n c\u00e1c \u1ea9n th\u00f4ng qua c\u00e1c d\u1eef ki\u1ec7n c\u1ee7a \u0111\u1ec1 b\u00e0i","explain":"<span class='basic_left'> G\u1ecdi s\u1ed1 h\u1ecdc sinh t\u1ed5 1, t\u1ed5 2, t\u1ed5 3 c\u1ee7a l\u1edbp 7A l\u1ea7n l\u01b0\u1ee3t l\u00e0 $x, y, z$ (h\u1ecdc sinh) ($x, y, x \\in \\mathbb{N}^{*}; x, y, z < 54$) <br\/> Do l\u1edbp 7A c\u00f3 54 h\u1ecdc sinh n\u00ean $x + y + z = 54$ <br\/> Do t\u1ed5 1 th\u00eam v\u00e0o 3 h\u1ecdc sinh, t\u1ed5 2 th\u00eam 2 h\u1ecdc sinh, t\u1ed5 3 b\u1edbt \u0111i 5 h\u1ecdc sinh th\u00ec s\u1ed1 h\u1ecdc sinh t\u1ed5 1, 2, 3 t\u1ec9 l\u1ec7 v\u1edbi 2, 3, 4 <br\/> N\u00ean ta c\u00f3: $ (x + 3):(y + 2):(z - 5) = 2 : 3 : 4 $ <br\/> $ \\Rightarrow \\dfrac{x+3}{2} = \\dfrac{y+2}{3} = \\dfrac{z-5}{4} = \\dfrac{(x+3)+(y+2)+(z-5)}{2+3+4} \\\\ = \\dfrac{x+y+z}{9} = \\dfrac{54}{9} = 6$ <br\/> Do \u0111\u00f3: $\\dfrac{x+3}{2} = 6 \\Rightarrow x + 3 = 2.6 = 12 \\Rightarrow x = 12 - 3 = 9 \\\\ \\dfrac{y+2}{3} = 6 \\Rightarrow y + 2 = 3.6 = 18 \\Rightarrow y = 18 - 2 = 16 \\\\ \\dfrac{z-5}{4} = 6 \\Rightarrow z - 5 = 4.6 = 24 \\Rightarrow z = 24 + 5 = 29 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 h\u1ecdc sinh t\u1ed5 1 l\u00e0 9, t\u1ed5 2 l\u00e0 16, t\u1ed5 3 l\u00e0 29 <\/span><\/span> <\/span>"}]}],"id_ques":344},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p s\u1ed1 \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["18"],["24"],["27"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" Chia s\u1ed1 $69$ th\u00e0nh ba ph\u1ea7n t\u1ec9 l\u1ec7 v\u1edbi c\u00e1c s\u1ed1 $\\dfrac{1}{2}; \\dfrac{2}{3}$ v\u00e0 $\\dfrac{3}{4}$. T\u00ecm ba s\u1ed1 \u0111\u00f3. <br\/><br\/> Ba ph\u1ea7n l\u1ea7n l\u01b0\u1ee3t l\u00e0: (input_;_input_;_input_)","hint":"","explain":" G\u1ecdi ba ph\u1ea7n c\u1ea7n t\u00ecm l\u1ea7n l\u01b0\u1ee3t l\u00e0 $x, y, z (> 0)$. <br\/> Theo \u0111\u1ec1 b\u00e0i, ta c\u00f3: $\\dfrac{x}{\\dfrac{1}{2}} = \\dfrac{y}{\\dfrac{2}{3}} = \\dfrac{z}{\\dfrac{3}{4}} = \\dfrac{x+y+z}{\\dfrac{1}{2}+\\dfrac{2}{3}+\\dfrac{3}{4}} = \\dfrac{69}{\\dfrac{23}{12}} = 36$ <br\/> Suy ra $ x = \\dfrac{1}{2}.36 = 18 \\\\ y = \\dfrac{2}{3}.36 = 24 \\\\ z = \\dfrac{3}{4}.36 = 27 $<br\/> <br\/> <span class='basic_pink'> V\u1eady ba ph\u1ea7n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $18; 24; 27$ <\/span><\/span>"}]}],"id_ques":345},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p s\u1ed1 \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["10"],["15"],["20"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ecm $x, y, z$ d\u01b0\u01a1ng bi\u1ebft: <br\/> $\\dfrac{x^{3}}{8} = \\dfrac{y^{3}}{27} = \\dfrac{z^{3}}{64}$ v\u00e0 $x^{2} + 2y^{2} - 3z^{2} = -650 $ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_;$y =$ _input_; $z=$_input_","explain":" Ta c\u00f3: $\\dfrac{x^{3}}{8} = \\dfrac{y^{3}}{27} = \\dfrac{z^{3}}{64} \\\\ \\Rightarrow \\left(\\dfrac{x}{2}\\right)^{3} = \\left(\\dfrac{y}{3}\\right)^{3} = \\left(\\dfrac{z}{4}\\right)^{3} \\\\ \\Rightarrow \\dfrac{x}{2} = \\dfrac{y}{3} = \\dfrac{z}{4} \\\\ \\Rightarrow \\dfrac{x^{2}}{4} = \\dfrac{y^{2}}{9} = \\dfrac{z^{2}}{16} $<br\/> Do \u0111\u00f3: $ \\dfrac{x^{2}}{4} = \\dfrac{y^{2}}{9} = \\dfrac{z^{2}}{16} = \\dfrac{x^{2}+2y^{2}-3z^{2}}{4+2.9-3.16} = \\dfrac{-650}{-26} = 25 $ <br\/> Suy ra $x^{2} = 100 \\Rightarrow x = \\pm 10 \\\\ y^{2} = 225 \\Rightarrow y = \\pm 15 \\\\ z^{2} = 400 \\Rightarrow z = \\pm 20 $ <br\/> M\u00e0 theo gi\u1ea3 thi\u1ebft x, y, z \u0111\u1ec1u d\u01b0\u01a1ng n\u00ean $x=10; y=15; z=20$ th\u1ecfa m\u00e3n \u0111\u1ec1 b\u00e0i <br\/> <br\/> <span class='basic_pink'> V\u1eady $\\begin{cases} x = 10 \\\\ y = 15 \\\\ z = 20 \\end{cases}$ <\/span><\/span>"}]}],"id_ques":346},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p s\u1ed1 \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["5"],["3"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" Cho $\\dfrac{x}{2} = \\dfrac{y}{3} = \\dfrac{z}{4}$ <br\/> <br\/> T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c <br\/> $P = \\dfrac{y+z-x}{x-y+z}$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> P = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"","explain":" Ta c\u00f3: $ \\dfrac{x}{2} = \\dfrac{y}{3} = \\dfrac{z}{4} = \\dfrac{y+z-x}{3+4-2} = \\dfrac{y+z-x}{5} (1) \\\\ \\dfrac{x}{2} = \\dfrac{y}{3} = \\dfrac{z}{4} = \\dfrac{x-y+z}{2-3+4} = \\dfrac{x-y+z}{3} (2)$ <br\/> T\u1eeb (1) v\u00e0 (2) suy ra $ \\dfrac{y+z-x}{5} = \\dfrac{x-y+z}{3} \\\\ \\Rightarrow \\dfrac{y+z-x}{x-y+z} = \\dfrac{5}{3} $ <br\/> <br\/> <span class='basic_pink'> K\u1ebft qu\u1ea3 l\u00e0 $\\dfrac{5}{3}$ <\/span><\/span>"}]}],"id_ques":347},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p s\u1ed1 \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["24"],["15"],["40"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" T\u00ecm c\u00e1c s\u1ed1 a, b, c bi\u1ebft: <br\/> $ 5a = 8b = 3c$ v\u00e0 $ a - 2b + c = 34 $ <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b>$a = $ _input_;$b =$ _input_; $c=$_input_","hint":" L\u00e0m xu\u1ea5t hi\u1ec7n t\u1ec9 l\u1ec7 th\u1ee9c b\u1eb1ng c\u00e1ch chia c\u00e1c s\u1ed1 c\u1ee7a bi\u1ec3u th\u1ee9c 5a = 8b = 3c cho BCNN(5; 8; 3) ","explain":" Ta c\u00f3: $ 5a = 8b = 3c$ Ta chia \u0111\u1eb3ng th\u1ee9c cho $BCNN(5; 8; 3) = 120 $ <br\/> $ \\Rightarrow \\dfrac{5a}{120} = \\dfrac{8b}{120} = \\dfrac{3c}{120} $$\\Rightarrow \\dfrac{a}{24} = \\dfrac{b}{15} = \\dfrac{c}{40} $ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau, ta \u0111\u01b0\u1ee3c:<br\/> $ \\dfrac{a}{24} = \\dfrac{b}{15} = \\dfrac{c}{40} = \\dfrac{2b}{30} = \\dfrac{a-2b+c}{24-30+40} = \\dfrac{34}{34} = 1 $ <br\/> Do \u0111\u00f3: $\\dfrac{a}{24} = 1 \\Rightarrow a = 24 \\\\ \\dfrac{b}{15} = 1 \\Rightarrow b = 15 \\\\ \\dfrac{c}{40} = 1 \\Rightarrow c = 40 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $a, b, c$ l\u00e0: $\\begin{cases} a = 24 \\\\ b = 15 \\\\ c = 40 \\end{cases}$ <\/span><\/span> <span class='basic_left'><br\/> <b> <u> Nh\u1eadn x\u00e9t <\/b> <\/u> <br\/> Mu\u1ed1n bi\u1ebfn \u0111\u1ed5i $mx=ny=pz$ th\u00e0nh m\u1ed9t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau <br\/> ta \u0111\u00e3 chia $mx, ny, pz$ cho BCNN $(m, n, p).$ <\/span>"}]}],"id_ques":348},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p s\u1ed1 \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["60"],["90"],["144"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" T\u00ecm c\u00e1c s\u1ed1 a, b, c bi\u1ebft: <br\/> $a +2b +5c = 960$ v\u00e0 $\\dfrac{a}{4} = \\dfrac{b}{6}, \\dfrac{b}{5} = \\dfrac{c}{8}$ <br\/> <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b>$a = $ _input_;$b =$ _input_; $c=$_input_ ","hint":" L\u00e0m xu\u1ea5t hi\u1ec7n t\u1ec9 l\u1ec7 th\u1ee9c, b\u1eb1ng c\u00e1ch \u0111\u01b0a m\u1eabu s\u1ed1 c\u1ee7a b \u1edf hai \u0111\u1eb3ng th\u1ee9c $\\dfrac{a}{4} = \\dfrac{b}{6}, \\dfrac{b}{5} = \\dfrac{c}{8}$ gi\u1ed1ng nhau","explain":" Ta c\u00f3: $\\dfrac{a}{4} = \\dfrac{b}{6} \\Rightarrow \\dfrac{a}{20} = \\dfrac{b}{30} (1) \\\\ \\dfrac{b}{5} = \\dfrac{c}{8} \\Rightarrow \\dfrac{b}{30} = \\dfrac{c}{48 } (2)$ <br\/> T\u1eeb (1) v\u00e0 (2) suy ra: $\\dfrac{a}{20} = \\dfrac{b}{30} = \\dfrac{c}{48} $ $\\Rightarrow \\dfrac{a}{20} = \\dfrac{2b}{60}= \\dfrac{5c}{240}$<br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a d\u00e3y t\u1ec9 s\u1ed1 b\u1eb3ng nhau ta \u0111\u01b0\u1ee3c <br\/> $ \\dfrac{a}{20} = \\dfrac{2b}{60}= \\dfrac{5c}{240} = \\dfrac{a+2b+5c}{20+60+240} = \\dfrac{960}{320} = 3$ <br\/> Do \u0111\u00f3: $\\dfrac{a}{20} = 3 \\Rightarrow a = 60 \\\\ \\dfrac{b}{30} = 3 \\Rightarrow b = 90 \\\\ \\dfrac{c}{48} = 3 \\Rightarrow c = 144 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $a, b, c$ l\u00e0: $\\begin{cases} a = 60 \\\\ b = 90 \\\\ c = 144 \\end{cases}$ <\/span><\/span> "}]}],"id_ques":349},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p s\u1ed1 \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" T\u00ecm $x$ bi\u1ebft: <br\/> $ (x - 20) : (x - 10) = (x + 40):(x + 70) $ ","select":["A. $30$ ","B. $ 40$ ","C. $50$","D. $60$"],"hint":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau","explain":" Ta c\u00f3: $ (x - 20) : (x - 10) = (x + 40):(x + 70)$ <br\/> Suy ra: $ \\dfrac{x-20}{x-10} = \\dfrac{x+40}{x+70}$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t d\u00e3y t\u1ec9 s\u1ed1 b\u1eb1ng nhau ta c\u00f3: <br\/> $ \\dfrac{x-20}{x-10} = \\dfrac{x+40}{x+70} = \\dfrac{(x-20)-(x+40)}{(x-10)-(x+70)} \\\\ = \\dfrac{x-20-x-40}{x-10-x-70} \\\\ = \\dfrac{-60}{-80} = \\dfrac{3}{4} $ <br\/> Suy ra: $\\dfrac{x-20}{x-10} = \\dfrac{3}{4} \\\\ \\Rightarrow \\dfrac{x-20}{3} = \\dfrac{x-10}{4} = \\dfrac{(x-20)-(x-10)}{3-4} \\\\ = \\dfrac{x-20-x+10}{3-4} = \\dfrac{-10}{-1} = 10 \\\\ \\Rightarrow \\dfrac{x-20}{3} = 10 \\\\ \\Rightarrow x - 20 = 30 \\\\ \\Rightarrow x = 50 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x $ l\u00e0: $50$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p s\u1ed1 \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":350}],"lesson":{"save":0,"level":3}}