{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["999"],["1000"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ednh nhanh <br\/> <br\/> $A = \\dfrac{1}{1 . 2} + \\dfrac{1}{2 . 3} + \\dfrac{1}{3 . 4} + ... + \\dfrac{1}{999 . 1000} = \\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}$ ","hint":"\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c $\\dfrac{1}{n.(n - 1)} = \\dfrac{1}{n} - \\dfrac{1}{n + 1}$ $(n \\in \\mathbb{N^*})$ ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c $\\dfrac{1}{n.(n - 1)} = \\dfrac{1}{n} - \\dfrac{1}{n + 1}$ \u0111\u1ec3 ph\u00e2n t\u00edch c\u00e1c ph\u00e2n s\u1ed1 tr\u00ean <br\/> <b> B\u01b0\u1edbc 2: <\/b> Tri\u1ec7t ti\u00eau c\u00e1c ph\u00e2n s\u1ed1 \u0111\u1ed1i nhau <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ecm k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align*} A &= \\dfrac{1}{1 . 2} + \\dfrac{1}{2 . 3} + \\dfrac{1}{3 . 4} + ... + \\dfrac{1}{999 . 1000} \\\\ &= \\dfrac{2 - 1}{1 . 2} + \\dfrac{3 - 2}{2 . 3} + \\dfrac{4 - 3}{3 . 4} + ... + \\dfrac{1000 - 999}{999 . 1000} \\\\ &= \\dfrac{2}{1 . 2} - \\dfrac{1}{1 . 2} + \\dfrac{3}{2 . 3} - \\dfrac{2}{2 . 3} + \\dfrac{4}{3 . 4} - \\dfrac{3}{3 . 4} + ... + \\dfrac{1000}{999 . 1000} - \\dfrac{999}{999 . 1000} \\\\ &= 1 - \\dfrac{1}{2}+ \\dfrac{1}{2} - \\dfrac{1}{3} + \\dfrac{1}{3} - \\dfrac{1}{4} + ... + \\dfrac{1}{999} - \\dfrac{1}{1000} \\\\ &= 1 - \\dfrac{1}{1000} \\\\ &= \\dfrac{999}{1000} \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 999; 1000 <\/span> <br\/><span class='basic_green'> <i> Nh\u1eadn x\u00e9t: C\u00f4ng th\u1ee9c $\\dfrac{1}{n.(n - 1)} = \\dfrac{1}{n} - \\dfrac{1}{n + 1}$ $(n \\in \\mathbb{N^*})$ gi\u00fap ta t\u00ednh nhanh \u0111\u01b0\u1ee3c t\u1ed5ng c\u00e1c ph\u00e2n s\u1ed1 vi\u1ebft theo quy lu\u1eadt v\u00ec \u0111\u00e3 l\u00e0m xu\u1ea5t hi\u1ec7n c\u00e1c s\u1ed1 \u0111\u1ed1i nhau <\/i> <\/span> "}]}],"id_ques":1641},{"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 $S = \\dfrac{1}{2^2} + \\dfrac{1}{3^2} + \\dfrac{1}{4^2} + \\dfrac{1}{5^2} + \\dfrac{1}{6^2}$ <br\/> <br\/>Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang? ","select":["A. S > 1 ","B. S = 1","C. S < 1"],"hint":"So s\u00e1nh $\\dfrac{1}{n^2}$ v\u1edbi $\\dfrac{1}{(n - 1) . n}$ ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> So s\u00e1nh m\u1ed7i ph\u00e2n s\u1ed1 c\u00f3 d\u1ea1ng $\\dfrac{1}{n^2}$ v\u1edbi ph\u00e2n s\u1ed1 $\\dfrac{1}{(n - 1) . n}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u1eeb b\u01b0\u1edbc 1 suy ra $S < \\dfrac{1}{1 . 2} + \\dfrac{1}{2 . 3} + ... + \\dfrac{1}{5 . 6}$ <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh t\u1ed5ng $\\dfrac{1}{1 . 2} + \\dfrac{1}{2 . 3} + ... + \\dfrac{1}{5 . 6}$ v\u00e0 so s\u00e1nh v\u1edbi 1 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> <br\/> Ta c\u00f3: <br\/> $\\dfrac{1}{2^2} < \\dfrac{1}{1 . 2}$ <br\/> $\\dfrac{1}{3^2} < \\dfrac{1}{2 . 3}$ <br\/> ......... <br\/> $\\dfrac{1}{6^2} < \\dfrac{1}{5 . 6}$ <br\/> $\\Rightarrow$ $ S < \\dfrac{1}{1 . 2} + \\dfrac{1}{2 . 3} + ... + \\dfrac{1}{5 . 6}$ <br\/> $\\begin{align*} & \\dfrac{1}{1 . 2} + \\dfrac{1}{2 . 3} + ... + \\dfrac{1}{5 . 6} \\\\ &= 1 - \\dfrac{1}{2} + \\dfrac{1}{2} - \\dfrac{1}{3} + ... + \\dfrac{1}{5} - \\dfrac{1}{6} \\\\ &= 1 - \\dfrac{1}{6} \\\\ &= \\dfrac{5}{6} \\end{align*}$ <br\/> $\\Rightarrow$ $ S < \\dfrac{5}{6}$ v\u00e0 $\\dfrac{5}{6} < 1$ <br\/> N\u00ean: $S = \\dfrac{1}{2^2} + \\dfrac{1}{3^2} + \\dfrac{1}{4^2} + \\dfrac{1}{5^2} + \\dfrac{1}{6^2} < 1$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: C. S < 1 <\/span> ","column":3}]}],"id_ques":1642},{"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 $S = \\dfrac{1}{2} + \\dfrac{1}{6} + \\dfrac{1}{12} + \\dfrac{1}{20} + \\dfrac{1}{30} + \\dfrac{1}{42} + \\dfrac{1}{56} + \\dfrac{1}{72} + \\dfrac{1}{90}$ <br\/><br\/> Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang? ","select":["A. S < 1 ","B. S = 1","C. S > 1"],"hint":"Ph\u00e2n t\u00edch c\u00e1c m\u1eabu s\u1ed1 th\u00e0nh t\u00edch c\u1ee7a hai s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Nh\u1eadn th\u1ea5y c\u00e1c s\u1ed1 2 = 1 . 2; 6 = 2 . 3; 12 = 3 . 4.... <br\/> N\u00ean $S = \\dfrac{1}{2} + \\dfrac{1}{6} + \\dfrac{1}{12} + \\dfrac{1}{20} + \\dfrac{1}{30} + \\dfrac{1}{42} + \\dfrac{1}{56} + \\dfrac{1}{72} + \\dfrac{1}{90} \\\\ = \\dfrac{1}{1 . 2} + \\dfrac{1}{2 . 3} + \\dfrac{1}{3 . 4} + \\dfrac{1}{4 . 5} + \\dfrac{1}{5 . 6} + ... + \\dfrac{1}{9 . 10}$ <br\/> T\u1eeb \u0111\u00f3 ta t\u00ednh \u0111\u01b0\u1ee3c t\u1ed5ng S sau \u0111\u00f3 so s\u00e1nh v\u1edbi 1 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> <br\/> Ta c\u00f3: <br\/> $\\begin{align*} S &= \\dfrac{1}{2} + \\dfrac{1}{6} + \\dfrac{1}{12} + \\dfrac{1}{20} + \\dfrac{1}{30} + \\dfrac{1}{42} + \\dfrac{1}{56} + \\dfrac{1}{72} + \\dfrac{1}{90} \\\\ &= \\dfrac{1}{1 . 2} + \\dfrac{1}{2 . 3} + \\dfrac{1}{3 . 4} + \\dfrac{1}{4 . 5} + \\dfrac{1}{5 . 6} + \\dfrac{1}{6 . 7} + \\dfrac{1}{7 . 8} + \\dfrac{1}{8 . 9} + \\dfrac{1}{9 . 10} \\\\ &= 1 - \\dfrac{1}{2} + \\dfrac{1}{2} - \\dfrac{1}{3} + \\dfrac{1}{3} - \\dfrac{1}{4} + \\dfrac{1}{4} - \\dfrac{1}{5} + \\dfrac{1}{5} - \\dfrac{1}{6} + \\dfrac{1}{6} - \\dfrac{1}{7} + \\dfrac{1}{7} - \\dfrac{1}{8} + \\dfrac{1}{8} - \\dfrac{1}{9} + \\dfrac{1}{9} - \\dfrac{1}{10} \\\\ &= 1 - \\dfrac{1}{10} \\\\ &= \\dfrac{9}{10} \\end{align*}$ <br\/> V\u00ec $\\dfrac{9}{10} < 1$ n\u00ean S < 1 <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A. S < 1 <\/span> <br\/> <span class='basic_green'> <i> Nh\u1eadn x\u00e9t: Kh\u00e9o l\u00e9o ph\u00e2n t\u00edch m\u1eabu s\u1ed1 th\u00e0nh t\u00edch c\u1ee7a hai s\u1ed1 t\u1ef1 nhi\u00ean t\u1eeb \u0111\u00f3 ph\u00e2n t\u00edch l\u00e0m xu\u1ea5t hi\u1ec7n c\u00e1c ph\u00e2n s\u1ed1 d\u1ea1ng $\\dfrac{1}{a} - \\dfrac{1}{b} + \\dfrac{1}{b} - \\dfrac{1}{c}$, tri\u1ec7t ti\u00eau c\u00e1c ph\u00e2n s\u1ed1 \u0111\u1ed1i, t\u1eeb \u0111\u00f3 ta t\u00ednh t\u1ed5ng m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng <\/i> <\/span> ","column":3}]}],"id_ques":1643},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["<"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"H\u00e3y \u0111i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng <br\/><br\/> $A = 4 + \\dfrac{1}{7^6} + \\dfrac{3}{7} + \\dfrac{4}{7^2} + \\dfrac{-441}{7^6} + \\dfrac{27}{7^5}$ <br\/> <br\/> $B = \\dfrac{147}{7^3} + 4 + \\dfrac{35}{7^7} + \\dfrac{4}{7^2} + \\dfrac{27}{7^5} + \\dfrac{-9}{7^9}$ <br\/> <br\/> A _input_ B ","hint":"Nh\u00f3m c\u00e1c s\u1ed1 h\u1ea1ng gi\u1ed1ng nhau th\u00e0nh m\u1ed9t nh\u00f3m, sau \u0111\u00f3 so s\u00e1nh c\u00e1c s\u1ed1 h\u1ea1ng c\u00f2n l\u1ea1i \u1edf A v\u00e0 B ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Nh\u1eadn th\u1ea5y c\u1ea3 A v\u00e0 B c\u00f3 m\u1ed9t s\u1ed1 s\u1ed1 h\u1ea1ng m\u1eabu s\u1ed1 gi\u1ed1ng nhau n\u00ean ta t\u00ecm c\u00e1ch bi\u1ebfn \u0111\u1ed5i \u0111\u1ec3 c\u1ea3 A v\u00e0 B xu\u1ea5t hi\u1ec7n nh\u1eefng s\u1ed1 h\u1ea1ng gi\u1ed1ng nhau. Khi \u0111\u00f3 ta ch\u1ec9 c\u1ea7n so s\u00e1nh c\u00e1c s\u1ed1 h\u1ea1ng c\u00f2n l\u1ea1i \u1edf A v\u00e0 B <br\/><b> B\u01b0\u1edbc 1: <\/b> R\u00fat g\u1ecdn c\u00e1c ph\u00e2n s\u1ed1 ch\u01b0a t\u1ed1i gi\u1ea3n \u1edf A v\u00e0 B <br\/> <b> B\u01b0\u1edbc 2: <\/b> Nh\u00f3m c\u00e1c s\u1ed1 h\u1ea1ng gi\u1ed1ng nhau \u1edf A v\u00e0 B <br\/> <b> B\u01b0\u1edbc 3: <\/b> So s\u00e1nh c\u00e1c s\u1ed1 h\u1ea1ng c\u00f2n l\u1ea1i \u1edf A v\u00e0 B, sau \u0111\u00f3 so s\u00e1nh A v\u00e0 B <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align*} A &= 4 + \\dfrac{1}{7^6} + \\dfrac{3}{7} + \\dfrac{4}{7^2} + \\dfrac{-441}{7^6} + \\dfrac{27}{7^5} \\\\ &= 4 + \\dfrac{1}{7^6} + \\dfrac{3}{7} + \\dfrac{4}{7^2} + \\dfrac{-441 : 49}{7^6 : 49} + \\dfrac{27}{7^5} \\\\ &= \\left( 4 + \\dfrac{27}{7^5} + \\dfrac{3}{7} + \\dfrac{4}{7^2} \\right) + \\dfrac{1}{7^6} + \\dfrac{-9}{7^4} \\end{align*}$ <br\/> $\\begin{align*} B &= \\dfrac{147}{7^3} + 4 + \\dfrac{35}{7^7} + \\dfrac{4}{7^2} + \\dfrac{27}{7^5} + \\dfrac{-9}{7^9} \\\\ &= \\dfrac{147 : 49}{7^3 : 49} + 4 + \\dfrac{35 : 7}{7^7 : 7} + \\dfrac{4}{7^2} + \\dfrac{27}{7^5} + \\dfrac{-9}{7^9} \\\\ &= \\dfrac{3}{7} + 4 + \\dfrac{5}{7^6} + \\dfrac{4}{7^2} + \\dfrac{27}{7^5} + \\dfrac{-9}{7^9} \\\\ &= \\left( 4 + \\dfrac{27}{7^5} + \\dfrac{3}{7} + \\dfrac{4}{7^2} \\right) + \\dfrac{5}{7^6} + \\dfrac{-9}{7^9} \\end{align*}$ <br\/> C\u00f3: $\\dfrac{1}{7^6} < \\dfrac{5}{7^6}$ (1) <br\/> $\\dfrac{9}{7^4} > \\dfrac{9}{7^9}$ $\\Rightarrow$ $\\dfrac{-9}{7^4} < \\dfrac{-9}{7^9}$ (2) <br\/> T\u1eeb (1) v\u00e0 (2) $\\Rightarrow$ $\\dfrac{1}{7^6} + \\dfrac{-9}{7^4} < \\dfrac{5}{7^6} + \\dfrac{-9}{7^9}$ <br\/> $\\Rightarrow$ $\\left( 4 + \\dfrac{27}{7^5} + \\dfrac{3}{7} + \\dfrac{4}{7^2} \\right) + \\dfrac{1}{7^6} + \\dfrac{-9}{7^4} < \\left( 4 + \\dfrac{27}{7^5} + \\dfrac{3}{7} + \\dfrac{4}{7^2} \\right) + \\dfrac{5}{7^6} + \\dfrac{-9}{7^9}$ <br\/> $\\Rightarrow$ A < B <br\/> <span class='basic_pink'> V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0: < <\/span> <br\/> <span class='basic_green'> <i> Nh\u1eadn x\u00e9t: Khi so s\u00e1nh hai bi\u1ec3u th\u1ee9c A, B th\u00f4ng th\u01b0\u1eddng ta kh\u00f4ng t\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c m\u00e0 so s\u00e1nh t\u1eebng s\u1ed1 h\u1ea1ng trong A v\u1edbi t\u1eebng s\u1ed1 h\u1ea1ng trong B <br\/> Ho\u1eb7c so s\u00e1nh m\u1ed9t nh\u00f3m s\u1ed1 h\u1ea1ng \u1edf A v\u1edbi 1 nh\u00f3m s\u1ed1 h\u1ea1ng \u1edf B <\/i><\/span> "}]}],"id_ques":1644},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-97"],["300"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ecm x bi\u1ebft: <br\/><br\/> $ \\left( \\dfrac{11}{12} + \\dfrac{11}{12 . 23} + \\dfrac{11}{23 . 34} + ... + \\dfrac{11}{89 . 100} \\right) + x = \\dfrac{2}{3}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0: $x = \\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}$ ","hint":"T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c trong ngo\u1eb7c sau \u0111\u00f3 t\u00ecm x nh\u01b0 b\u00ecnh th\u01b0\u1eddng ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh $\\dfrac{11}{12} + \\dfrac{11}{12 . 23} + \\dfrac{11}{23 . 34} + ... + \\dfrac{11}{89 . 100}$ <br\/> Theo c\u00f4ng th\u1ee9c $\\dfrac{a}{n . (n + a)} = \\dfrac{1}{n} - \\dfrac{1}{n + a}$ ($a, n \\in \\mathbb{N^*}$) <br\/> <b> B\u01b0\u1edbc 2: <\/b> Coi x l\u00e0 s\u1ed1 h\u1ea1ng ch\u01b0a bi\u1ebft, mu\u1ed1n t\u00ecm s\u1ed1 h\u1ea1ng ch\u01b0a bi\u1ebft l\u1ea5y t\u1ed5ng tr\u1eeb s\u1ed1 h\u1ea1ng \u0111\u00e3 bi\u1ebft <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $ \\dfrac{11}{12} + \\dfrac{11}{12 . 23} + \\dfrac{11}{23 . 34} + ... + \\dfrac{11}{89 . 100} \\\\ = \\dfrac{12 - 1}{12} + \\dfrac{23 - 12}{12 . 23} + \\dfrac{34 - 23}{23 . 34} + ... + \\dfrac{100 - 89}{89 . 100} \\\\ = - \\dfrac{1}{12} + \\dfrac{1}{12} - \\dfrac{1}{23} + \\dfrac{1}{23} - \\dfrac{1}{34} + ... + \\dfrac{1}{99} - \\dfrac{1}{100} \\\\ = 1 - \\dfrac{1}{100} \\\\ = \\dfrac{99}{100}$ <br\/> $\\begin{align*} \\Rightarrow \\dfrac{99}{100} + x &= \\dfrac{2}{3} \\\\ x &= \\dfrac{2}{3} - \\dfrac{99}{100} \\\\ x &= \\dfrac{200}{300} - \\dfrac{297}{300} \\\\ x &= \\dfrac{-97}{300} \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: -97; 300 <\/span> "}]}],"id_ques":1645},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $\\left[\\begin{array}{l}{x=\\dfrac{-13}{36}}\\\\{x = \\dfrac{7}{12}}\\end{array}\\right.$","B. $\\left[\\begin{array}{l}{x=\\dfrac{13}{36}}\\\\ {x = \\dfrac{-7}{12}}\\end{array}\\right.$","C. $\\left[\\begin{array}{l}{x=\\dfrac{-13}{36}}\\\\{x = \\dfrac{5}{12}}\\end{array}\\right.$"],"ques":"T\u00ecm x bi\u1ebft: <br\/><br\/> $ \\dfrac{4}{3} - | 6x - \\dfrac{2}{3}| = \\dfrac{-3}{2}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0: $x$ = ? ho\u1eb7c $x$ = ?","hint":"B\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i r\u1ed3i t\u00ecm x ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Coi $| 6x - \\dfrac{2}{3}|$ l\u00e0 s\u1ed1 tr\u1eeb ch\u01b0a bi\u1ebft <br\/> Mu\u1ed1n t\u00ecm s\u1ed1 tr\u1eeb ch\u01b0a bi\u1ebft ta l\u1ea5y s\u1ed1 b\u1ecb tr\u1eeb tr\u1eeb hi\u1ec7u <br\/> <b> B\u01b0\u1edbc 2: <\/b> B\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i theo c\u00f4ng th\u1ee9c <br\/> $\\left[ \\begin{align} & x=1 \\\\ & x=2 \\end{align} \\right.$ <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $\\begin{align*} \\dfrac{4}{3} - | 6x - \\dfrac{2}{3}| &= \\dfrac{-3}{2} \\\\ |6x - \\dfrac{2}{3}| &= \\dfrac{4}{3} - \\dfrac{-3}{2} \\\\ |6x - \\dfrac{2}{3}| &= \\dfrac{8}{6} - \\dfrac{-9}{6} \\\\ |6x - \\dfrac{2}{3}| &= \\dfrac{8 - (-9)}{6} \\\\ |6x - \\dfrac{2}{3}| &= \\dfrac{17}{6} \\end{align*}$ <br\/> $\\Rightarrow$ $\\left[ \\begin{align} & 6x - \\dfrac{2}{3} = \\dfrac{17}{6} \\\\ & 6x - \\dfrac{2}{3} = -\\dfrac{17}{6} \\end{align} \\right.$ <br\/> $\\Rightarrow$ $\\left[ \\begin{align} & 6x = \\dfrac{17}{6} + \\dfrac{2}{3} \\\\ & 6x = -\\dfrac{17}{6} + \\dfrac{2}{3} \\end{align} \\right.$ <br\/> $\\Rightarrow$ $\\left[ \\begin{align} & 6x = \\dfrac{7}{2} \\\\ & 6x = \\dfrac{-13}{6} \\end{align} \\right.$ <br\/> $\\Rightarrow$ $\\left[ \\begin{align} & x = \\dfrac{7}{12} \\\\ & x = \\dfrac{-13}{36} \\end{align} \\right.$<br\/> <span class='basic_green'> <i> L\u01b0u \u00fd: Khi b\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i l\u01b0u \u00fd x\u00e9t c\u1ea3 hai tr\u01b0\u1eddng h\u1ee3p, h\u1ecdc sinh hay m\u1eafc sai l\u1ea7m l\u00e0 ch\u1ec9 x\u00e9t tr\u01b0\u1eddng h\u1ee3p l\u1edbn h\u01a1n 0 d\u1eabn \u0111\u1ebfn thi\u1ebfu \u0111\u00e1p \u00e1n <\/i><\/span> "}]}],"id_ques":1646},{"time":24,"part":[{"title":"N\u1ed1i bi\u1ec3u th\u1ee9c \u1edf c\u1ed9t b\u00ean tr\u00e1i v\u1edbi s\u1ed1 ho\u1eb7c ph\u00e2n s\u1ed1 \u1edf c\u1ed9t b\u00ean ph\u1ea3i \u0111\u1ec3 \u0111\u01b0\u1ee3c \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","audio":"","temp":"matching","correct":[["3","4","1","2"]],"list":[{"point":10,"image":"","left":["$1) \\hspace{1cm} \\dfrac{-2}{5} + \\dfrac{3}{-4} + \\dfrac{6}{7} + \\dfrac{3}{4} + \\dfrac{2}{5}$ ","$2) \\hspace{1cm} \\dfrac{-1}{8} + \\dfrac{7}{9} + \\dfrac{-7}{8} + \\dfrac{6}{7} + \\dfrac{2}{14}$ ","$3) \\hspace{1cm} \\dfrac{5}{11} + \\dfrac{16}{22} + \\dfrac{-12}{4} + \\dfrac{-2}{11}$ ","$4) \\hspace{1cm} \\dfrac{7}{23} + \\dfrac{-10}{18} + \\dfrac{-4}{9} + \\dfrac{16}{23}$ "],"right":[" $A. -2$ "," $B. 0$ "," $C. \\dfrac{6}{7}$ ","$D. \\dfrac{7}{9}$"],"top":100,"hint":" R\u00fat g\u1ecdn r\u1ed3i nh\u00f3m c\u00e1c ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu","explain":" <span class='basic_left'> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\dfrac{-2}{5} + \\dfrac{3}{-4} + \\dfrac{6}{7} + \\dfrac{3}{4} + \\dfrac{2}{5} \\\\ = \\left( \\dfrac{-2}{5} + \\dfrac{2}{5} \\right) + \\left( \\dfrac{3}{-4} + \\dfrac{3}{4} \\right) + \\dfrac{6}{7} \\\\ = \\dfrac{6}{7} $ <br\/><br\/> $\\dfrac{-1}{8} + \\dfrac{7}{9} + \\dfrac{-7}{8} + \\dfrac{6}{7} + \\dfrac{2}{14} \\\\ = \\left( \\dfrac{-1}{8} + \\dfrac{-7}{8} \\right) + \\left( \\dfrac{6}{7} + \\dfrac{2}{14} \\right) + \\dfrac{7}{9} \\\\ = -1 + \\left( \\dfrac{12}{14} + \\dfrac{2}{14} \\right) + \\dfrac{7}{9} \\\\ = \\dfrac{7}{9} $ <br\/><br\/> $\\dfrac{5}{11} + \\dfrac{16}{22} + \\dfrac{-12}{4} + \\dfrac{-2}{11} \\\\ = \\left( \\dfrac{5}{11} + \\dfrac{-2}{11} + \\dfrac{16}{22} \\right) + (-3) \\\\ = \\left( \\dfrac{5}{11} + \\dfrac{-2}{11} + \\dfrac{8}{11} \\right) + (-3) \\\\ = 1 + (-3) \\\\ = -2 $ <br\/><br\/> $\\dfrac{7}{23} + \\dfrac{-10}{18} + \\dfrac{-4}{9} + \\dfrac{16}{23} \\\\ = \\left( \\dfrac{7}{23} + \\dfrac{16}{23} \\right) + \\left(-10){18} + \\dfrac{-4}{9} \\right) \\\\ = 1 + \\left( \\dfrac{-10}{18} + \\dfrac{-8}{18} \\right) \\\\ = 1 + (-1) \\\\ = 0 $ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: 1 - C; 2 - D; 3 - A; 4 - B <\/span> "}]}],"id_ques":1647},{"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":"M\u1ed9t c\u1eeda h\u00e0ng l\u01b0\u01a1ng th\u1ef1c bu\u1ed5i s\u00e1ng b\u00e1n \u0111\u01b0\u1ee3c $\\dfrac{3}{5}$ t\u1ed5ng s\u1ed1 g\u1ea1o. Bu\u1ed5i chi\u1ec1u c\u1eeda h\u00e0ng b\u00e1n \u0111\u01b0\u1ee3c $\\dfrac{1}{4}$ s\u1ed1 g\u1ea1o c\u00f2n l\u1ea1i c\u1ee7a bu\u1ed5i s\u00e1ng. Bu\u1ed5i t\u1ed1i b\u00e1n \u0111\u01b0\u1ee3c $\\dfrac{1}{2}$ s\u1ed1 g\u1ea1o c\u00f2n l\u1ea1i c\u1ee7a bu\u1ed5i chi\u1ec1u. H\u1ecfi c\u1eeda h\u00e0ng c\u00f2n l\u1ea1i bao nhi\u00eau ph\u1ea7n g\u1ea1o? ","select":["A. $\\dfrac{-7}{20}$ s\u1ed1 g\u1ea1o ","B. $\\dfrac{3}{20}$ s\u1ed1 g\u1ea1o","C. $\\dfrac{3}{10}$ s\u1ed1 g\u1ea1o ","D. $\\dfrac{3}{15}$ s\u1ed1 g\u1ea1o"],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n g\u1ea1o c\u00f2n l\u1ea1i sau khi b\u00e1n bu\u1ed5i s\u00e1ng <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n g\u1ea1o c\u1eeda h\u00e0ng b\u00e1n b\u00e1n bu\u1ed5i chi\u1ec1u so v\u1edbi s\u1ed1 g\u1ea1o c\u1ee7a c\u1eeda h\u00e0ng <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n g\u1ea1o c\u00f2n l\u1ea1i sau khi b\u00e1n bu\u1ed5i chi\u1ec1u <br\/> <b> B\u01b0\u1edbc 4: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n g\u1ea1o b\u00e1n bu\u1ed5i t\u1ed1i so v\u1edbi t\u1ed5ng s\u1ed1 g\u1ea1o c\u1ee7a c\u1eeda h\u00e0ng <br\/> <b> B\u01b0\u1edbc 5: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n g\u1ea1o c\u00f2n l\u1ea1i c\u1ee7a c\u1eeda h\u00e0ng sau khi b\u00e1n bu\u1ed5i t\u1ed1i <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> <br\/> S\u1ed1 ph\u1ea7n g\u1ea1o c\u00f2n l\u1ea1i sau khi b\u00e1n bu\u1ed5i s\u00e1ng l\u00e0: <br\/> $1 - \\dfrac{3}{5} = \\dfrac{2}{5}$ (s\u1ed1 g\u1ea1o) <br\/> S\u1ed1 ph\u1ea7n g\u1ea1o c\u1eeda h\u00e0ng b\u00e1n bu\u1ed5i chi\u1ec1u l\u00e0: <br\/> $\\dfrac{1}{4} . \\dfrac{2}{5} = \\dfrac{1}{10}$ (s\u1ed1 g\u1ea1o) <br\/> S\u1ed1 ph\u1ea7n g\u1ea1o c\u00f2n l\u1ea1i sau khi b\u00e1n bu\u1ed5i chi\u1ec1u l\u00e0: <br\/> $\\dfrac{2}{5} - \\dfrac{1}{10} = \\dfrac{3}{10}$ (s\u1ed1 g\u1ea1o) <br\/> S\u1ed1 ph\u1ea7n g\u1ea1o c\u1eeda h\u00e0ng b\u00e1n bu\u1ed5i t\u1ed1i l\u00e0: <br\/> $\\dfrac{1}{2} . \\dfrac{3}{10} = \\dfrac{3}{20}$ (s\u1ed1 g\u1ea1o) <br\/> S\u1ed1 ph\u1ea7n g\u1ea1o c\u00f2n l\u1ea1i c\u1ee7a c\u1eeda h\u00e0ng l\u00e0: <br\/> $\\dfrac{3}{10} - \\dfrac{3}{20} = \\dfrac{3}{20}$ (s\u1ed1 g\u1ea1o) <br\/> \u0110\u00e1p s\u1ed1: $\\dfrac{3}{20}$ s\u1ed1 g\u1ea1o ","column":2}]}],"id_ques":1648},{"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":"C\u1ea3 3 v\u00f2i n\u01b0\u1edbc c\u00f9ng ch\u1ea3y v\u00e0o b\u1ec3 th\u00ec sau 3 gi\u1edd m\u1edbi \u0111\u1ea7y b\u1ec3. N\u1ebfu ri\u00eang v\u00f2i 1 ch\u1ea3y th\u00ec sau 15 gi\u1edd \u0111\u1ea7y b\u1ec3. N\u1ebfu ri\u00eang v\u00f2i 2 ch\u1ea3y sau 12 gi\u1edd \u0111\u1ea7y b\u1ec3. H\u1ecfi v\u00f2i 3 ch\u1ea3y m\u1ed9t m\u00ecnh trong 1 gi\u1edd \u0111\u01b0\u1ee3c bao nhi\u00eau ph\u1ea7n b\u1ec3? <br\/> \u0110\u00e1p \u00e1n l\u00e0: ","select":["A. $\\dfrac{11}{60}$ b\u1ec3 ","B. $\\dfrac{17}{20}$ b\u1ec3","C. $\\dfrac{3}{20}$ b\u1ec3 ","D. $\\dfrac{49}{60}$ b\u1ec3"],"hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n b\u1ec3 v\u00f2i 1 ch\u1ea3y \u0111\u01b0\u1ee3c trong 1 gi\u1edd <br\/> <b> B\u01b0\u1edbc 2: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n b\u1ec3 v\u00f2i hai ch\u1ea3y \u0111\u01b0\u1ee3c trong 1 gi\u1edd <br\/> <b> B\u01b0\u1edbc 3: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n b\u1ec3 c\u1ea3 3 v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c trong 1 gi\u1edd <br\/> <b> B\u01b0\u1edbc 4: <\/b> T\u00ednh s\u1ed1 ph\u1ea7n b\u1ec3 v\u00f2i 3 ch\u1ea3y \u0111\u01b0\u1ee3c trong 1 gi\u1edd <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> <br\/> S\u1ed1 ph\u1ea7n b\u1ec3 v\u00f2i 1 ch\u1ea3y \u0111\u01b0\u1ee3c trong 1 gi\u1edd l\u00e0: <br\/> 1 : 15 = $\\dfrac{1}{15}$ (b\u1ec3) <br\/> S\u1ed1 ph\u1ea7n b\u1ec3 v\u00f2i 2 ch\u1ea3y \u0111\u01b0\u1ee3c trong 1 gi\u1edd l\u00e0: <br\/> 1 : 12 = $\\dfrac{1}{12}$ (b\u1ec3) <br\/> S\u1ed1 ph\u1ea7n b\u1ec3 c\u1ea3 3 v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c trong 1 gi\u1edd l\u00e0: <br\/> 1 : 3 = $\\dfrac{1}{3}$ (b\u1ec3) <br\/> S\u1ed1 ph\u1ea7n b\u1ec3 v\u00f2i 3 ch\u1ea3y trong 1 gi\u1edd l\u00e0: <br\/> $\\dfrac{1}{3} - \\dfrac{1}{15} - \\dfrac{1}{12} = \\dfrac{11}{60}$ (b\u1ec3) <br\/> \u0110\u00e1p s\u1ed1: $\\dfrac{11}{60}$ b\u1ec3 <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: A <\/span> ","column":2}]}],"id_ques":1649},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"],["3"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" R\u00fat g\u1ecdn ph\u00e2n s\u1ed1 $\\dfrac{\\dfrac{1}{13 . 16} + \\dfrac{1}{14 . 17}}{\\dfrac{1}{13 . 15} + \\dfrac{1}{14 . 16} + \\dfrac{1}{15 . 17}}$ <br\/><br\/> \u0110\u00e1p \u00e1n l\u00e0: $\\dfrac{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}$ ","hint":" S\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c $\\dfrac{a}{n . (n + a)} = \\dfrac{1}{n} - \\dfrac{1}{n + a}$ ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> S\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c $\\dfrac{a}{n . (n + a)} = \\dfrac{1}{n} - \\dfrac{1}{n + a}$ t\u00e1ch m\u1ed7i ph\u00e2n s\u1ed1 tr\u00ean th\u00e0nh hi\u1ec7u c\u1ee7a hai ph\u00e2n s\u1ed1 <br\/> <b> B\u01b0\u1edbc 2: <\/b> R\u00fat g\u1ecdn, t\u00ecm k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $\\begin{align*} & \\dfrac{\\dfrac{1}{13 . 16} + \\dfrac{1}{14 . 17}}{\\dfrac{1}{13 . 15} + \\dfrac{1}{14 . 16} + \\dfrac{1}{15 . 17}} \\\\ &= \\dfrac{\\dfrac{1}{3} . 3 . \\left( \\dfrac{1}{13 . 16} + \\dfrac{1}{14 . 17} \\right)}{ \\dfrac{1}{2} . 2 . \\left( \\dfrac{1}{13 . 15} + \\dfrac{1}{14 . 16} + \\dfrac{1}{15 . 17} \\right)} \\\\ &= \\dfrac{ \\dfrac{1}{3} . \\left( \\dfrac{3}{13 . 16} + \\dfrac{3}{14 . 17} \\right)}{\\dfrac{1}{2}. \\left( \\dfrac{2}{13 . 15} + \\dfrac{2}{14 . 16} + \\dfrac{2}{15 . 17} \\right)} \\\\ &= \\dfrac{\\dfrac{1}{3} . \\left( \\dfrac{1}{13} - \\dfrac{1}{16} + \\dfrac{1}{14} - \\dfrac{1}{17} \\right)}{\\dfrac{1}{2} . \\left( \\dfrac{1}{13} - \\dfrac{1}{15} + \\dfrac{1}{14} - \\dfrac{1}{16} + \\dfrac{1}{15} - \\dfrac{1}{17} \\right)} \\\\ &= \\dfrac{\\dfrac{1}{3} . \\left( \\dfrac{1}{13} - \\dfrac{1}{16} + \\dfrac{1}{14} - \\dfrac{1}{17} \\right)}{\\dfrac{1}{2} . \\left( \\dfrac{1}{13} + \\dfrac{1}{14} - \\dfrac{1}{16} - \\dfrac{1}{17} \\right)} \\\\ &= \\dfrac{1}{3} : \\dfrac{1}{2} \\\\ &= \\dfrac{2}{3} \\end{align*}$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 2; 3 <\/span> <br\/> <span class='basic_green'> <i> Nh\u1eadn x\u00e9t: Trong tr\u01b0\u1eddng h\u1ee3p b\u00e0i cho ph\u00e2n s\u1ed1 $\\dfrac{1}{n . (n + a)}$ ta ch\u01b0a s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c $\\dfrac{a}{n . (n + a)} = \\dfrac{1}{n} - \\dfrac{1}{n + a}$ ngay \u0111\u01b0\u1ee3c m\u00e0 ta ph\u1ea3i th\u00eam b\u1edbt l\u00e0m xu\u1ea5t hi\u1ec7n a \u1edf t\u1eed s\u1ed1 r\u1ed3i m\u1edbi s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c tr\u00ean <\/i><\/span> "}]}],"id_ques":1650}],"lesson":{"save":0,"level":3}}