{"segment":[{"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":[[["0"],["-2"],["1"],["-3"],["3"],["-5"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"Cho bi\u1ec3u th\u1ee9c A = $\\dfrac{4}{n + 1}$; $n \\in \\mathbb{Z}$. T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a n \u0111\u1ec3 gi\u00e1 tr\u1ecb c\u1ee7a A l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean. <br\/> \u0110\u00e1p \u00e1n l\u00e0: $n \\in ${_input_; _input_; _input_; _input_; _input_; _input_}","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u0110i\u1ec1u ki\u1ec7n \u0111\u1ec3 A l\u00e0 s\u1ed1 nguy\u00ean th\u00ec n + 1 l\u00e0 \u01b0\u1edbc c\u1ee7a 4 <br\/> T\u1eeb \u0111\u00f3 t\u00ecm c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a n th\u1ecfa m\u00e3n <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> \u0110\u1ec3 $A = \\dfrac{4}{n + 1}$ l\u00e0 s\u1ed1 nguy\u00ean th\u00ec 4 $\\vdots$ (n + 1) hay n + 1$\\in$ \u01af(4) <br\/> M\u00e0 4 c\u00f3 c\u00e1c \u01b0\u1edbc l\u00e0: 1; -1; 2; -2; 4; -4 <br\/> $\\Rightarrow$ n + 1 $\\in$ {1; -1; 2; -2; 4; -4} <br\/> Khi n + 1 = 1 $\\Rightarrow$ n = 0 <br\/> Khi n + 1 = -1 $\\Rightarrow$ n = -2 <br\/> Khi n + 1 = 2 $\\Rightarrow$ n = 1 <br\/> Khi n + 1 = -2 $\\Rightarrow$ n = -3 <br\/> Khi n + 1 = 4 $\\Rightarrow$ n = 3 <br\/> Khi n + 1 = -4 $\\Rightarrow$ n = -5 <br\/> V\u1eady v\u1edbi n $\\in$ {0; -2; 1; -3; 3; -5 } th\u00ec A c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 s\u1ed1 nguy\u00ean <br\/> <span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 0; -2; 1; -3; 3; -5 <\/span> "}]}],"id_ques":1441},{"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":[[["-2"],["0"],["1"],["3"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"Cho bi\u1ec3u th\u1ee9c B = $\\dfrac{5}{2n - 1}$; $n \\in \\mathbb{Z}$. T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a n \u0111\u1ec3 gi\u00e1 tr\u1ecb c\u1ee7a B l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean . <br\/> \u0110\u00e1p \u00e1n l\u00e0: $n \\in ${_input_; _input_; _input_; _input_} (t\u1eadp h\u1ee3p gi\u00e1 tr\u1ecb c\u1ee7a n \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp theo th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n)","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u0110i\u1ec1u ki\u1ec7n \u0111\u1ec3 B l\u00e0 s\u1ed1 nguy\u00ean th\u00ec 2n - 1 l\u00e0 \u01b0\u1edbc c\u1ee7a 5 <br\/> T\u1eeb \u0111\u00f3 t\u00ecm c\u00e1c gi\u00e1 tr\u1ecb c\u1ee7a n th\u1ecfa m\u00e3n <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> \u0110\u1ec3 $B = \\dfrac{5}{2n - 1}$ l\u00e0 s\u1ed1 nguy\u00ean th\u00ec 5 $\\vdots$ (2n - 1) hay 2n - 1$\\in$ \u01af(5) <br\/>M\u00e0 5 c\u00f3 c\u00e1c \u01b0\u1edbc l\u00e0: 1; -1; 5; -5 <br\/> $\\Rightarrow$ 2n - 1 $\\in$ {1; -1; 5; -5} <br\/> Khi 2n - 1 = 1 $\\Rightarrow$ n = 1 <br\/> Khi 2n - 1 = -1 $\\Rightarrow$ n = 0 <br\/> Khi 2n - 1 = 5 $\\Rightarrow$ n = 3 <br\/> Khi 2n - 1 = -5 $\\Rightarrow$ n = -2 <br\/> V\u1eady v\u1edbi n $\\in$ {0; 1; 3; -2 } th\u00ec B c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 s\u1ed1 nguy\u00ean<br\/>T\u1eadp h\u1ee3p gi\u00e1 tr\u1ecb n th\u1ecfa m\u00e3n \u0111\u1ea7u b\u00e0i \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp theo th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n l\u00e0: n $\\in$ {-2; 0; 1; 3}<br\/> <span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: -2; 0; 1; 3 <\/span> "}]}],"id_ques":1442},{"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":[[["8"],["42"],["18"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"H\u00e3y \u0111i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng <br\/> $\\dfrac{2}{7}$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">28<\/div><\/div> = <div class=\"frac123\"><div class=\"ts\">12<\/div><div class=\"ms\">_input_<\/div><\/div>= <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">63<\/div><\/div>","hint":"D\u1ef1a v\u00e0o kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1 b\u1eb1ng nhau","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> G\u1ecdi c\u00e1c s\u1ed1 c\u1ea7n t\u00ecm l\u1ea7n l\u01b0\u1ee3t l\u00e0 a, b, c <br\/> $\\dfrac{2}{7} = \\dfrac{a}{28} = \\dfrac{12}{b} = \\dfrac{c}{63}$ <br\/> Cho l\u1ea7n l\u01b0\u1ee3t c\u00e1c ph\u00e2n s\u1ed1 $\\dfrac{a}{28}; \\dfrac{12}{b}; \\dfrac{c}{63}$ b\u1eb1ng ph\u00e2n s\u1ed1 $\\dfrac{2}{7}$ \u0111\u1ec3 t\u00ecm a, b, c <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi c\u00e1c s\u1ed1 c\u1ea7n t\u00ecm l\u1ea7n l\u01b0\u1ee3t l\u00e0 a, b, c <br\/> Khi \u0111\u00f3: $\\dfrac{2}{7} = \\dfrac{a}{28} = \\dfrac{12}{b} = \\dfrac{c}{63}$ <br\/> V\u00ec: $\\dfrac{2}{7} = \\dfrac{a}{28}$ n\u00ean 2 . 28 = 7 . a <br\/> Do \u0111\u00f3: $a = \\dfrac{2 . 28}{7} = 8$ <br\/> V\u00ec $\\dfrac{2}{7} = \\dfrac{12}{b}$ n\u00ean 2 . b = 7 . 12 <br\/> Do \u0111\u00f3: $b = \\dfrac{7 . 12}{2} = 42$ <br\/> V\u00ec: $\\dfrac{2}{7} = \\dfrac{c}{63}$ n\u00ean 2 . 63 = 7 . c <br\/> Do \u0111\u00f3: $c = \\dfrac{2 . 63}{7} = 18$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0: 8; 42; 18 <\/span> "}]}],"id_ques":1443},{"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":" Cho c\u00e1c ph\u00e2n s\u1ed1 sau: $\\dfrac{3}{4}; \\dfrac{8}{6}; \\dfrac{11}{25}; \\dfrac{21}{28}$ <br\/> Trong c\u00e1c ph\u00e2n s\u1ed1 tr\u00ean c\u00f3 c\u00e1c ph\u00e2n s\u1ed1 n\u00e0o b\u1eb1ng nhau? <br\/><br\/> H\u00e3y ch\u1ecdn c\u1eb7p ph\u00e2n s\u1ed1 b\u1eb1ng nhau trong c\u00e1c c\u1eb7p ph\u00e2n s\u1ed1 sau:","select":["A. $\\dfrac{21}{18}$ v\u00e0 $\\dfrac{3}{4}$","B.$\\dfrac{21}{18}$ v\u00e0 $\\dfrac{11}{25}$","C. $\\dfrac{3}{4}$ v\u00e0 $\\dfrac{11}{25}$ ","D. $\\dfrac{11}{25}$ v\u00e0 $\\dfrac{21}{18}$"],"hint":"","explain":"<span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> X\u00e9t ph\u00e2n s\u1ed1 $\\dfrac{3}{4}$ v\u00e0 ph\u00e2n s\u1ed1 $\\dfrac{8}{6}$ <br\/> C\u00f3: 3 . 6 = 18 $\\neq$ 32 = 4 . 8 n\u00ean $\\dfrac{3}{4} \\neq \\dfrac{8}{6}$ <br\/> Ph\u00e2n s\u1ed1: $\\dfrac{3}{4}$ v\u00e0 $\\dfrac{11}{25}$ <br\/> C\u00f3: 3 . 25 = 75 $\\neq$ 44 = 4 . 11 n\u00ean $\\dfrac{3}{4} \\neq \\dfrac{11}{25}$ <br\/> Ph\u00e2n s\u1ed1: $\\dfrac{3}{4}$ v\u00e0 $\\dfrac{21}{28}$ <br\/> C\u00f3: 3 . 28 = 84 = 21 . 4 n\u00ean $\\dfrac{3}{4} = \\dfrac{21}{28}$ <br\/> Ph\u00e2n s\u1ed1: $\\dfrac{8}{6}$ v\u00e0 $\\dfrac{11}{25}$ <br\/> C\u00f3: 8 . 25 = 200 $\\neq$ 66 = 6 . 11 n\u00ean $\\dfrac{8}{6} \\neq \\dfrac{21}{28}$ <br\/> Ph\u00e2n s\u1ed1: $\\dfrac{8}{6}$ v\u00e0 $\\dfrac{21}{28}$ <br\/> C\u00f3: 8 . 28 = 224 $\\neq$ 126 = 6 . 21 n\u00ean $\\dfrac{8}{6} = \\dfrac{21}{28}$ <br\/> Ph\u00e2n s\u1ed1: $\\dfrac{11}{25}$ v\u00e0 $\\dfrac{21}{28}$ <br\/> C\u00f3: 11 . 28 = 308 $\\neq$ 525 = 25 . 21 n\u00ean $\\dfrac{11}{25} \\neq \\dfrac{21}{28}$ <br\/> <span class='basic_pink'> V\u1eady c\u1eb7p ph\u00e2n s\u1ed1 b\u1eb1ng nhau l\u00e0: $\\dfrac{3}{4} = \\dfrac{21}{28}$ <\/span> ","column":2}]}],"id_ques":1444},{"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 $x \\in \\mathbb{Z}$ bi\u1ebft $\\dfrac{x - 3}{4} = \\dfrac{15}{20}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. x = 3","B. x = 0","C. x = -3","D. x = 6"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn: <\/span><br\/> D\u1ef1a v\u00e0o kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1 b\u1eb1ng nhau <br\/> X\u00e9t t\u00edch ch\u00e9o (x - 3) . 20 = 4 . 15 t\u1eeb \u0111\u00f3 ta t\u00ecm \u0111\u01b0\u1ee3c x <br\/><\/span><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> <br\/> V\u00ec $\\dfrac{x - 3}{4} = \\dfrac{15}{20}$ n\u00ean: <br\/> $\\begin{align*}(x - 3) . 20 &= 4 . 15 \\\\ (x - 3). 20 &= 60 \\\\ x - 3 &= 60 : 20 \\\\ x - 3 &= 3 \\\\ x &= 3 + 3 \\\\ x &= 6 \\end{align*}$ <br\/> V\u1eady v\u1edbi x = 6 th\u00ec ph\u00e2n s\u1ed1 $\\dfrac{x - 3}{4} = \\dfrac{15}{20}$ <br\/> <span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: D. x = 6 <\/span>","column":2}]}],"id_ques":1445},{"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":" H\u00e3y ch\u1ecdn t\u1eadp h\u1ee3p A g\u1ed3m c\u00e1c s\u1ed1 nguy\u00ean x th\u1ecfa m\u00e3n $\\dfrac{-25}{4} < x < 1$ <br\/> \u0110\u00e1p \u00e1n l\u00e0:","select":["A. A = {-5; -4; -3; -2; 1}","B. A = {-6; -5; -4; -3; -2; -1; 0}","C. A = {-7; -6; -5; -4; -3; -2; -1; 0}","D. A = {-6; -5; -4; -3; -2; -1; 0; 1}"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn: <\/span><br\/><b> B\u01b0\u1edbc 1: <\/b> Ch\u1ecdn ph\u00e2n s\u1ed1 l\u1edbn h\u01a1n ph\u00e2n s\u1ed1 $\\dfrac{-25}{4}$ v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb nguy\u00ean (gi\u1ea3 s\u1eed l\u00e0 a) khi \u0111\u00f3 $\\dfrac{-25}{4} < a$ <br\/> <b> B\u01b0\u1edbc 2:<\/b> Li\u1ec7t k\u00ea c\u00e1c s\u1ed1 nguy\u00ean x th\u1ecfa m\u00e3n: $a \\leq x < 1$ <br\/> C\u00e1c s\u1ed1 \u0111\u00f3 ch\u00ednh l\u00e0 c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p A <br\/><\/span><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> <br\/> Ta c\u00f3: -25 < -24 n\u00ean $\\dfrac{-25}{4} < \\dfrac{-24}{4}$ <br\/> M\u00e0 $\\dfrac{-24}{4} = -6$ n\u00ean $\\dfrac{-25}{4} < -6$ <br\/> Do \u0111\u00f3: $-6 \\leq x < 1$ $\\Rightarrow x \\in$ {-6; -5; -4; -3; -2; -1; 0} <br\/> Hay A = {-6; -5; -4; -3; -2; -1; 0} <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B <\/span>","column":2}]}],"id_ques":1446},{"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"],["8"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ecm s\u1ed1 nguy\u00ean x, y th\u1ecfa m\u00e3n $\\dfrac{x - 3}{y-2} = \\dfrac{3}{2}$ v\u00e0 x - y = 4 <br\/> V\u1eady x = _input_; y = _input_","hint":"D\u1ef1a v\u00e0o kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1 b\u1eb1ng nhau","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Bi\u1ebfn \u0111\u1ed1i \u0111\u1eb3ng th\u1ee9c (x - 3) . 2 = (y - 2) . 3 <br\/> Chuy\u1ec3n nh\u1eefng s\u1ed1 h\u1ea1ng ch\u1ee9a x, y v\u1ec1 v\u1ebf tr\u00e1i sau \u0111\u00f3 bi\u1ebfn \u0111\u1ed5i \u0111\u1eb3ng th\u1ee9c v\u1ec1 d\u1ea1ng x - y = ..... <br\/> <b> B\u01b0\u1edbc 2: <\/b> Thay x - y = 4 v\u00e0o \u0111\u1eb3ng th\u1ee9c tr\u00ean \u0111\u1ec3 t\u00ecm x ho\u1eb7c y <br\/> <b> B\u01b0\u1edbc 3: <\/b> Thay x ho\u1eb7c y v\u1eeba t\u00ecm \u0111\u01b0\u1ee3c \u1edf b\u01b0\u1edbc 2 v\u00e0o \u0111\u1eb3ng th\u1ee9c x - y = 4 \u0111\u1ec3 t\u00ecm s\u1ed1 c\u00f2n l\u1ea1i <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec $\\dfrac{x - 3}{y-2} = \\dfrac{3}{2}$ n\u00ean ta c\u00f3: <br\/> $\\begin{align*}(x - 3) . 2 & = (y - 2) . 3 \\\\ 2x - 6 &= 3y - 6 \\\\ 2x - 3y &= -6 + 6 \\\\ 2x - 2y - y &= 0 \\\\ 2.(x - y) &= y (1) \\end{align*} $ <br\/> Thay x - y = 4 v\u00e0o (1) ta \u0111\u01b0\u1ee3c: <br\/> 2 . 4 = y hay y = 8 <br\/> Thay y = 8 v\u00e0o \u0111\u1eb3ng th\u1ee9c x - y = 4 $\\Rightarrow$ x = 4 + y = 4 + 8 = 12 <br\/> V\u1eady v\u1edbi x = 12, y = 8 th\u00ec $\\dfrac{x - 3}{y-2} = \\dfrac{3}{2}$ <br\/> <span class='basic_pink'>C\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0: 12; 8 <\/span> "}]}],"id_ques":1447},{"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":[[["3"],["2"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ecm s\u1ed1 nguy\u00ean x, y th\u1ecfa m\u00e3n $\\dfrac{x - 1}{y + 1} = \\dfrac{2}{3}$ v\u00e0 x - y = 1 <br\/> V\u1eady x = _input_; y = _input_","hint":"D\u1ef1a v\u00e0o kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1 b\u1eb1ng nhau","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Bi\u1ebfn \u0111\u1ed1i \u0111\u1eb3ng th\u1ee9c (x - 1) . 3 = (y + 1) . 2 <br\/> Chuy\u1ec3n nh\u1eefng s\u1ed1 h\u1ea1ng ch\u1ee9a x, y v\u1ec1 v\u1ebf tr\u00e1i sau \u0111\u00f3 bi\u1ebfn \u0111\u1ed5i \u0111\u1eb3ng th\u1ee9c v\u1ec1 d\u1ea1ng x - y = ..... <br\/> <b> B\u01b0\u1edbc 2: <\/b> Thay x - y = 1 v\u00e0o \u0111\u1eb3ng th\u1ee9c tr\u00ean \u0111\u1ec3 t\u00ecm x ho\u1eb7c y <br\/> <b> B\u01b0\u1edbc 3: <\/b> Thay x ho\u1eb7c y v\u1eeba t\u00ecm \u0111\u01b0\u1ee3c \u1edf b\u01b0\u1edbc 2 v\u00e0o \u0111\u1eb3ng th\u1ee9c x - y = 1 \u0111\u1ec3 t\u00ecm s\u1ed1 c\u00f2n l\u1ea1i <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> V\u00ec $\\dfrac{x - 1}{y + 1} = \\dfrac{2}{3}$ n\u00ean ta c\u00f3: <br\/> $\\begin{align*}(x - 1) . 3 & = (y + 1) . 2 \\\\ 3x - 3 &= 2y + 2 \\\\ 3x - 2y &= 2 + 3 \\\\ 2x + x - 2y &= 5 \\\\ 2(x - y) &= 5 - x (1) \\end{align*} $ <br\/> Thay x - y = 1 v\u00e0o (1) ta \u0111\u01b0\u1ee3c: <br\/> 2 . 1 = 5 - x hay x = 3 <br\/> Thay x = 3 v\u00e0o \u0111\u1eb3ng th\u1ee9c x - y = 1 $\\Rightarrow$ y = x - 1 = 3 - 1 = 2 <br\/> V\u1eady v\u1edbi x = 3, y = 2 th\u00ec $\\dfrac{x - 1}{y + 1} = \\dfrac{2}{3}$ <br\/> <span class='basic_pink'>C\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0: 3; 2 <\/span> "}]}],"id_ques":1448},{"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":[[["-4"],["-2"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"Cho $F = \\dfrac{2n + 7}{n + 3}$ . T\u00ecm c\u00e1c s\u1ed1 nguy\u00ean n \u0111\u1ec3 F c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 s\u1ed1 nguy\u00ean.<br\/> V\u1eady n = _input_; _input_","hint":"\u0110\u1ec3 F c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 s\u1ed1 nguy\u00ean th\u00ec (2n + 7) $\\vdots$ (n + 3)","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> \u0110\u1ec3 F c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 s\u1ed1 nguy\u00ean th\u00ec (2n + 7) $\\vdots$ (n + 3) <br\/> <b> B\u01b0\u1edbc 1: <\/b> Bi\u1ebfn \u0111\u1ed5i 2n + 7 v\u1ec1 d\u1ea1ng 2n + 7 = a.(n + 3) + b <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ecm n? <br\/> \u0110\u1ec3 (2n + 7) $\\vdots$ (n + 3) th\u00ec b $\\vdots$ (n + 3) t\u1eeb \u0111\u00f3 ta t\u00ecm \u0111\u01b0\u1ee3c n <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> \u0110\u1ec3 $F = \\dfrac{2n + 7}{n + 3}$ c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean th\u00ec: <br\/> $(2n + 7) \\vdots (n + 3)$ <br\/> M\u00e0 2n + 7 = 2n + 6 + 1 = 2(n + 3) + 1 <br\/> M\u00e0 2(n + 3) $\\vdots$ n + 3 <br\/>N\u00ean \u0111\u1ec3 2n + 7 $\\vdots$ n + 3 th\u00ec 1 $\\vdots$ n + 3 <br\/> 1 c\u00f3 c\u00e1c \u01b0\u1edbc l\u00e0 1 v\u00e0 -1 n\u00ean: <br\/> Khi n + 3 = 1 $\\Rightarrow$ n = -2 <br\/> Khi n + 3 = -1 $\\Rightarrow$ n = -4 <br\/> V\u1eady khi n = -2 ho\u1eb7c n = -4 th\u00ec $F = \\dfrac{2n + 7}{n + 3}$ c\u00f3 gi\u00e1 tr\u1ecb l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean <br\/> <span class='basic_pink'> C\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0: -4; -2 <\/span> "}]}],"id_ques":1449},{"time":14,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["56"],["120"]]],"list":[{"point":10,"width":90,"type_input":"","input_hint":["frac"],"ques":"T\u00ecm ph\u00e2n s\u1ed1 b\u1eb1ng ph\u00e2n s\u1ed1 $\\dfrac{7}{15}$ bi\u1ebft t\u1ed5ng c\u1ee7a t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 b\u1eb1ng 176 . <br\/> \u0110\u00e1p \u00e1n l\u00e0: <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"D\u1ef1a v\u00e0o kh\u00e1i ni\u1ec7m ph\u00e2n s\u1ed1 b\u1eb1ng nhau","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> G\u1ecdi t\u1eed s\u1ed1 c\u1ee7a ph\u00e2n s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 a <br\/> Khi \u0111\u00f3 m\u1eabu s\u1ed1 l\u00e0: 176 - a <br\/> <b> B\u01b0\u1edbc 2: <\/b> V\u00ec ph\u00e2n s\u1ed1 c\u1ea7n t\u00ecm b\u1eb1ng ph\u00e2n s\u1ed1 $\\dfrac{7}{15}$ n\u00ean ta c\u00f3: <br\/> 7 . (176 - a) = 15 . a <br\/> T\u1eeb \u0111\u00f3 ta t\u00ecm \u0111\u01b0\u1ee3c a <br\/> <b> B\u01b0\u1edbc 3: <\/b> Thay a v\u00e0o \u0111\u1ec3 t\u00ecm m\u1eabu s\u1ed1 c\u1ee7a ph\u00e2n s\u1ed1 \u0111\u00f3 <br\/> <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> G\u1ecdi t\u1eed s\u1ed1 c\u1ee7a ph\u00e2n s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 a $(a \\neq 176)$ <br\/> V\u00ec t\u1ed5ng c\u1ee7a t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 b\u1eb1ng 176 n\u00ean m\u1eabu s\u1ed1 l\u00e0: 176 - a <br\/> V\u1eady ph\u00e2n s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 $\\dfrac{a}{176 - a}$ <br\/> V\u00ec $\\dfrac{a}{176 - a} = \\dfrac{7}{15}$ n\u00ean: <br\/> $\\begin{align*}7 . (176 - a) &= 15 . a \\\\ 1232 - 7a &= 15a \\\\ 15a + 7a &= 1232 \\\\ 22a &= 1232 \\\\ a &= 56 \\end{align*}$ <br\/> $\\Rightarrow$ M\u1ea5u s\u1ed1 l\u00e0: 176 - 56 = 120"}]}],"id_ques":1450}],"lesson":{"save":0,"level":3}}