{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" Cho t\u1ec9 l\u1ec7 th\u1ee9c $ \\dfrac{5x - 2y}{3x + 4y} = \\dfrac{3}{4} $ (v\u1edbi $3x + 4y \\neq 0$). T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a t\u1ec9 s\u1ed1 $\\dfrac{x}{y} (y \\neq 0)$ ","select":["A. $\\dfrac{x}{y} = \\dfrac{11}{20}$ ","B. $\\dfrac{x}{y} = \\dfrac{20}{11}$ ","C. $\\dfrac{x}{y} = \\dfrac{3}{4}$ ","D. $\\dfrac{x}{y} = \\dfrac{4}{3}$ "],"hint":"\u00c1p d\u1ee5ng: $\\dfrac{a}{b} = \\dfrac{c}{d} \\Rightarrow ad = bc $ ","explain":" Theo t\u00ednh ch\u1ea5t c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c ta c\u00f3: <br\/> $ \\dfrac{5x - 2y}{3x + 4y} = \\dfrac{3}{4} \\\\ \\Rightarrow 4(5x - 2y) = 3(3x + 4y) \\\\ \\Rightarrow 20x - 8y = 9x + 12y \\\\ \\Rightarrow 20x - 9x = 8y + 12y \\\\ \\Rightarrow 11x = 20y \\\\ \\Rightarrow \\dfrac{x}{y} = \\dfrac{20}{11} (y \\neq 0) $ <br\/> V\u1eady $\\dfrac{x}{y} = \\dfrac{20}{11}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":291},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":" T\u00ecm $x $ trong t\u1ec9 l\u1ec7 th\u1ee9c sau: $ \\dfrac{3x+2}{5x+7} = \\dfrac{3x-1}{5x+1} $ ","select":["A. $ x = 3 $ ","B. $ x = -3 $ ","C. $ x = -5 $ ","D. $ x = 5 $ "],"hint":" $ \\dfrac{a}{b} = \\dfrac{c}{d} \\Rightarrow ad = bc$ ","explain":" <span class='basic_left'> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c ta c\u00f3: <br\/> $ \\dfrac{3x+2}{5x+7} = \\dfrac{3x-1}{5x+1} \\\\ \\Rightarrow (3x + 2)(5x + 1) = (5x + 7)(3x - 1) \\\\ \\Rightarrow 3x(5x + 1) + 2(5x + 1) = 5x(3x - 1) + 7(3x - 1) \\\\ \\Rightarrow 15x^{2} + 3x + 10x + 2 = 15x^{2} - 5x + 21x - 7 \\\\ \\Rightarrow 13x + 2 = 16x - 7 \\\\ \\Rightarrow 13x - 16x = -2 - 7 \\\\ \\Rightarrow -3x = -9 \\\\ \\Rightarrow x = 3 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a x l\u00e0 $ 3 $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span>","column":2}]}],"id_ques":292},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["70"],["40"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" T\u00ecm $x, y$ bi\u1ebft: $\\dfrac{x}{7} = \\dfrac{y}{4}$ v\u00e0 $x - y = 30$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x $= _input_; $y$ = _input_","hint":" \u0110\u1eb7t \u1ea9n ph\u1ee5: $\\dfrac{x}{7} = \\dfrac{y}{4} = k $ v\u00e0 bi\u1ec3u di\u1ec5n x, y theo k r\u1ed3i th\u1ebf v\u00e0o gi\u1ea3 thi\u1ebft th\u1ee9 2 ","explain":" Ta c\u00f3: $\\dfrac{x}{7} = \\dfrac{y}{4}$ (1) v\u00e0 $x - y = 30$ (2) <br\/> T\u1eeb (1): \u0110\u1eb7t $\\dfrac{x}{7} = \\dfrac{y}{4} = k \\Rightarrow \\begin{cases} x = 7k \\\\ y = 4k \\end{cases} $ <br\/> Thay $x = 7k; y = 4k$ v\u00e0o (2) ta \u0111\u01b0\u1ee3c: <br\/> $7k - 4k = 30 \\Rightarrow 3k = 30 \\Rightarrow k = 10 $ <br\/> Suy ra $\\begin{cases} x = 7.10 = 70 \\\\ y = 4.10 = 40 \\end{cases} $ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x, y$ l\u00e0 $ \\begin{cases} x = 70 \\\\ y = 40 \\end{cases} $ <\/span><\/span>"}]}],"id_ques":293},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-2"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" T\u00ecm $x$ trong t\u1ec9 l\u1ec7 th\u1ee9c: $ \\dfrac{12-7x}{-13} = \\dfrac{4-3x}{-5} $ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b>$ x $= _input_","hint":" $ \\dfrac{a}{b} = \\dfrac{c}{d} \\Rightarrow ad = bc $ ","explain":"\u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c ta c\u00f3: <br\/> $ \\dfrac{12-7x}{-13} = \\dfrac{4-3x}{-5} \\\\ \\Rightarrow (-5).(12 - 7x) = (-13).(4 - 3x) \\\\ \\Rightarrow -60 + 35x = -52 + 39x \\\\ \\Rightarrow 35x - 39x = 60 - 52 \\\\ \\Rightarrow -4x = 8 \\\\ \\Rightarrow x = \\dfrac{8}{-4} = -2 $ <br\/> <br\/> <span class='basic_pink'> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ l\u00e0 $ -2 $ <\/span><\/span>"}]}],"id_ques":294},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"Cho t\u1ec9 l\u1ec7 th\u1ee9c $ \\dfrac{a}{b+c} = \\dfrac{b}{a+c} = \\dfrac{c}{a+b} ( a ,b , c \\neq 0)$ <br\/> T\u00ednh $M = \\dfrac{b+c}{a} + \\dfrac{a+c}{b} + \\dfrac{a+b}{c} $ ","select":["A. $ -3 $ ","B. $ 3 $ ","C. $ 6 $ ","D. $ -4 $ "],"hint":" C\u1ed9ng th\u00eam 1 v\u00e0o c\u00e1c v\u1ebf c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c r\u1ed3i quy \u0111\u1ed3ng l\u00e0m xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed chung","explain":" <span class='basic_left'> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c ta c\u00f3: <br\/> <br\/> $ \\dfrac{a}{b+c} = \\dfrac{b}{a+c} = \\dfrac{c}{a+b} \\\\ \\Rightarrow \\dfrac{a}{b+c} + 1 = \\dfrac{b}{a+c} + 1 = \\dfrac{c}{a+b} + 1 \\\\ \\Rightarrow \\dfrac{a+b+c}{b+c} = \\dfrac{a+b+c}{a+c} = \\dfrac{a+b+c}{a+b} (1) $ <br\/> Nh\u1eadn th\u1ea5y 3 ph\u00e2n s\u1ed1 c\u00f3 t\u1eed s\u1ed1 b\u1eb1ng nhau (a+b+c) m\u00e0 3 ph\u00e2n s\u1ed1 b\u1eb1ng nhau n\u00ean m\u1eabu s\u1ed1 c\u1ee7a ch\u00fang c\u0169ng b\u1eb1ng nhau. <br\/> $\\Leftrightarrow b + c = a + c = a + b \\\\ \\Leftrightarrow a = b = c $ <br\/> Do \u0111\u00f3: $M = \\dfrac{b+c}{a} + \\dfrac{a+c}{b} + \\dfrac{a+b}{c} \\\\ = \\dfrac{2a}{a} + \\dfrac{2b}{b} + \\dfrac{2c}{c} \\\\ = 2 + 2 + 2 \\\\ = 6 $<br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a M l\u00e0 $ 6 $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span>","column":2}]}],"id_ques":295},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai6/lv3/img\/2.jpg' \/><\/center> Cho $\\dfrac{2x+3}{5x+2} = \\dfrac{4x+5}{10x+2}$, th\u00ec $x$ b\u1eb1ng: ","select":["A. $ x = 1 $ ","B. $ x = 4 $ ","C. $ x = 5 $ ","D. $ x = -1 $ "],"hint":" $ \\dfrac{a}{b} = \\dfrac{c}{d} \\Rightarrow ad = bc$ ","explain":" <span class='basic_left'> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c ta c\u00f3: <br\/> <br\/> $ \\dfrac{2x+3}{5x+2} = \\dfrac{4x+5}{10x+2} \\\\ \\Rightarrow (2x + 3)(10x + 2) = (5x + 2)(4x + 5) \\\\ \\Rightarrow 2x(10x + 2) + 3(10x + 2) = 5x(4x + 5) + 2(4x + 5) \\\\ \\Rightarrow 20x^{2} + 4x + 30x + 6 = 20x^{2} + 25x + 8x + 10 \\\\ \\Rightarrow 34x + 6 = 33x + 10 \\\\ \\Rightarrow 34x - 33x = -6 + 10 \\\\ \\Rightarrow x = 4 $ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a $x$ l\u00e0 $ 4 $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span>","column":2}]}],"id_ques":296},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":" Cho ba s\u1ed1 $2; 3; 5$. T\u00ecm $x \\in \\mathbb{Q}$ v\u1edbi $2 < x < 5$, sao cho $x$ c\u00f9ng v\u1edbi ba s\u1ed1 tr\u00ean l\u1eadp \u0111\u01b0\u1ee3c th\u00e0nh m\u1ed9t t\u1ec9 l\u1ec7 th\u1ee9c (m\u1ed7i s\u1ed1 ch\u1ec9 ch\u1ecdn m\u1ed9t l\u1ea7n). ","select":["A. $x = \\dfrac{10}{3}$ ","B. $ x = \\dfrac{6}{5}$","C. $x = \\dfrac{15}{2}$","D. C\u1ea3 ba \u0111\u00e1p \u00e1n \u0111\u1ec1u \u0111\u00fang"],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> \u0110\u1ec3 ki\u1ec3m tra xem b\u1ed1n s\u1ed1 $a, b , c, d$ \u0111\u00e3 x\u1eafp x\u1ebfp theo th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n c\u00f3 l\u1eadp th\u00e0nh m\u1ed9t t\u1ec9 l\u1ec7 th\u1ee9c hay kh\u00f4ng ta l\u00e0m nh\u01b0 sau: <br\/> $\\bullet$ N\u1ebfu $a < b < 0 < c < d$ th\u00ec ta ch\u1ec9 c\u1ea7n so s\u00e1nh hai c\u1eb7p s\u1ed1 sau: <br\/> $a.b$ v\u00e0 $c.d \\quad + \\quad a.c$ v\u00e0 $b.d$ <br\/> $\\bullet$ N\u1ebfu c\u1ea3 b\u1ed1n s\u1ed1 c\u00f9ng d\u1ea5u th\u00ec ta ch\u1ec9 c\u1ea7n so s\u00e1nh m\u1ed9t c\u1eb7p s\u1ed1 <br\/> $a.d$ v\u00e0 $b.c$ <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Do 2;3; 5; x c\u00f9ng d\u1ea5u n\u00ean ta c\u00f3 c\u00e1c tr\u01b0\u1eddng h\u1ee3p sau <br\/> Tr\u01b0\u1eddng h\u1ee3p 1: $2.x = 3.5\\Leftrightarrow x = \\dfrac{15}{2}$ $\\notin \\left( 2;5 \\right) \\Rightarrow$ lo\u1ea1i <br\/> Tr\u01b0\u1eddng h\u1ee3p 2: $3.x = 2.5\\Leftrightarrow x = \\dfrac{10}{3}$ $\\in \\left( 2;5 \\right) \\Rightarrow$ th\u1ecfa m\u00e3n <br\/> Tr\u01b0\u1eddng h\u1ee3p 3: $5.x = 3.2\\Leftrightarrow x = \\dfrac{6}{5}$ $\\notin \\left( 2;5 \\right) \\Rightarrow$ lo\u1ea1i <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":2}]}],"id_ques":297},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"T\u00ecm s\u1ed1 nguy\u00ean $x$ m\u00e0 th\u00eam v\u00e0o t\u1eed v\u00e0 b\u1edbt \u1edf m\u1eabu c\u1ee7a ph\u00e2n s\u1ed1 $\\dfrac{26}{39}$ ta \u0111\u01b0\u1ee3c m\u1ed9t ph\u00e2n s\u1ed1 m\u1edbi c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng $\\dfrac{6}{7}$","select":["A. $x = 6$ ","B. $x = 7$ ","C. $x = 13$ ","D. $x = 4$ "],"explain":" Th\u00eam v\u00e0o t\u1eed v\u00e0 b\u1edbt \u1edf m\u1eabu c\u1ee7a ph\u00e2n s\u1ed1 $\\dfrac{26}{39}$ ta \u0111\u01b0\u1ee3c m\u1ed9t ph\u00e2n s\u1ed1 $ \\dfrac{26 + x}{39 - x}$ <br\/> Ph\u00e2n s\u1ed1 m\u1edbi c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng $\\dfrac{6}{7}$ $\\Leftrightarrow \\dfrac{26 + x}{39 - x} = \\dfrac{6}{7} \\\\ \\Rightarrow 7.(26 + x) = 6.(39 - x) \\\\ \\Rightarrow 182 + 7x = 234 - 6x \\\\ \\Rightarrow 7x + 6x = -182 + 234 \\\\ \\Rightarrow 13x = 52 \\\\ \\Rightarrow x = \\dfrac{52}{13} = 4$ <br\/> V\u1eady gi\u00e1 tr\u1ecb c\u1ee7a x l\u00e0 $4$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span><\/span> ","column":2}]}],"id_ques":298},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" Cho t\u1ec9 l\u1ec7 th\u1ee9c $ \\dfrac{x - y}{x + 2y} = \\dfrac{3}{4} $ (v\u1edbi $x + 2y \\neq 0$). T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a t\u1ec9 s\u1ed1 $\\dfrac{x}{y} (y \\neq 0)$ ","select":["A. $\\dfrac{x}{y} = \\dfrac{1}{10}$ ","B. $\\dfrac{x}{y} = \\dfrac{3}{8}$ ","C. $\\dfrac{x}{y} = 10$ ","D. $\\dfrac{x}{y} = \\dfrac{8}{3}$ "],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> \u00c1p d\u1ee5ng: $\\dfrac{a}{b} = \\dfrac{c}{d} \\Rightarrow ad = bc $<\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Theo t\u00ednh ch\u1ea5t c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c ta c\u00f3: <br\/> $ \\dfrac{x - y}{x + 2y} = \\dfrac{3}{4} \\\\ \\Rightarrow 4(x - y) = 3(x + 2y) \\\\ \\Rightarrow 4x - 4y = 3x + 6y \\\\ \\Rightarrow 4x - 3x = 6y + 4y \\\\ \\Rightarrow x = 10y \\\\ \\Rightarrow \\dfrac{x}{y} = 10 $ <br\/> V\u1eady $\\dfrac{x}{y} = 10 $<br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":299},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["21"],["5"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" \u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 c\u00f3 t\u1ec9 l\u1ec7 th\u1ee9c: <br\/> <br\/> $ \\dfrac{4}{5} : 1\\dfrac{2}{5} = 2\\dfrac{2}{5} : $ <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t: $ a : b = c : d \\Rightarrow d = bc : a $ ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> D\u1ea1ng 3. T\u00ecm s\u1ed1 h\u1ea1ng ch\u01b0a bi\u1ebft c\u1ee7a m\u1ed9t t\u1ec9 l\u1ec7 th\u1ee9c <\/b> <br\/> <i> <u> Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i: <\/i> <\/u> <br\/> $\\bullet$ Mu\u1ed1n t\u00ecm m\u1ed9t ngo\u1ea1i t\u1ec9 ch\u01b0a bi\u1ebft, ta l\u1ea5y t\u00edch c\u00e1c trung t\u1ec9 chia cho ngo\u1ea1i t\u1ec9 kia.<br\/> $\\bullet$ Mu\u1ed1n t\u00ecm m\u1ed9t trung t\u1ec9 ch\u01b0a bi\u1ebft, ta l\u1ea5y t\u00edch c\u00e1c ngo\u1ea1i t\u1ec9 chia cho trung t\u1ec9 kia. <br\/> * <i> Ch\u1eb3ng h\u1ea1n, <\/i> trong t\u1ec9 l\u1ec7 th\u1ee9c $\\dfrac{a}{b} = \\dfrac{c}{d}$ \u0111\u00e3 bi\u1ebft $a, c, d$ th\u00ec $b = \\dfrac{ad}{c}$ <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> G\u1ecdi s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 x<br\/> $ \\dfrac{4}{5} : 1\\dfrac{2}{5} = 2\\dfrac{2}{5} : x$ $\\Leftrightarrow \\dfrac{4}{5} : \\dfrac{7}{5} = \\dfrac{12}{5} : x$ <br\/> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u1ee7a t\u1ec9 l\u1ec7 th\u1ee9c ta c\u00f3: <br\/> <br\/> $ \\dfrac{4}{5} : \\dfrac{7}{5} = \\dfrac{12}{5} : x \\\\ \\Rightarrow \\dfrac{4}{5}x = \\dfrac{12}{5} . \\dfrac{7}{5} \\\\ \\Rightarrow \\dfrac{4}{5}x = \\dfrac{84}{25} \\\\ \\Rightarrow x = \\dfrac{84}{25} : \\dfrac{4}{5} \\\\ \\Rightarrow x = \\dfrac{21}{5} $ <br\/> <br\/> <span class='basic_pink'> K\u1ebft qu\u1ea3 ph\u1ea3i \u0111i\u1ec1n l\u00e0 $\\dfrac{21}{5}$ <\/span><\/span>"}]}],"id_ques":300}],"lesson":{"save":0,"level":3}}