{"common":{"save":0,"post_id":"797","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"1491","post_id":"797","mon_id":"0","chapter_id":"0","question":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","options":{"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":[[["97"],["1560"]]],"list":[{"point":10,"width":50,"ques":"R\u00fat g\u1ecdn ph\u00e2n s\u1ed1 sau: <br\/> $\\dfrac{5^2 . 6^{11} . 16^2 + 6^2 . 12^6 . 15^2}{2 . 6^{12} . 10^4 - 81^2 . 960^3}$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"\u0110\u01b0a t\u1ea5t c\u1ea3 v\u1ec1 d\u1ea1ng l\u0169y th\u1eeba c\u01a1 s\u1ed1 2, c\u01a1 s\u1ed1 3 v\u00e0 c\u01a1 s\u1ed1 5","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u01b0a t\u1ea5t c\u1ea3 v\u1ec1 d\u1ea1ng l\u0169y th\u1eeba c\u01a1 s\u1ed1 2, c\u01a1 s\u1ed1 3 v\u00e0 c\u01a1 s\u1ed1 5 <br\/> <b> B\u01b0\u1edbc 2: <\/b> Nh\u00f3m nh\u1eefng l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 ra ngo\u00e0i, m\u1ed7i l\u0169y th\u1eeba l\u1eaby v\u1edbi s\u1ed1 m\u0169 nh\u1ecf nh\u1ea5t c\u1ee7a n\u00f3 <br\/> <b> B\u01b0\u1edbc 3: <\/b> R\u00fat g\u1ecdn nh\u1eefng nh\u00e2n t\u1eed chung \u1edf t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 <br\/> <b> B\u01b0\u1edbc 4: <\/b> T\u00ednh to\u00e1n 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*} & \\dfrac{5^2 . 6^{11} . 16^2 + 6^2 . 12^6 . 15^2}{2 . 6^{12} . 10^4 - 81^2 . 960^3}\\\\ &= \\dfrac{5^2 . (2 . 3)^{11} . (2^4)^2 + (3 . 2)^2 . (2^2 . 3)^{6} . (3 . 5)^{2}}{2 . (2 . 3)^{12} . (2 . 5)^4 - (3^4)^2 . (2^6 . 3 . 5)^3} \\\\ &= \\dfrac{5^2 . 2^{11} . 3^{11} . 2^8 + 3^2 . 2^2 . 2^{12} . 3^6 . 3^2 . 5^2}{2 . 2^{12} . 3^{12} . 2^4 . 5^4 - 3^8 . 2^{18} . 3^3 . 5^3} \\\\ &= \\dfrac{2^{19} . 3^{11} . 5^2 + 2^{14} . 3^{10} . 5^2}{2^{17} . 3^{12} . 5^4 - 2^{18} . 3^{11} . 5^3} \\\\ &= \\dfrac{2^{14} . 3^{10} . 5^2 . (2^5 . 3 + 1)}{2^{17} . 3^{11} . 5^3 . (3 . 5 - 2)} \\\\ &= \\dfrac{97}{2^3 . 3 . 5 . 13} \\\\ &= \\dfrac{97}{1560} \\end{align*}$<br\/> <span class='basic_green'> <i> Nh\u1eadn x\u00e9t: Th\u00f4ng th\u01b0\u1eddng khi l\u00e0m c\u00e1c b\u00e0i to\u00e1n d\u1ea1ng l\u0169y th\u1eeba nh\u01b0 tr\u00ean ta th\u01b0\u1eddng \u0111\u01b0a t\u1ea5t c\u1ea3 c\u00e1c l\u0169y th\u1eeba v\u1ec1 c\u01a1 s\u1ed1 l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1 sau \u0111\u00f3 bi\u1ebfn \u0111\u1ed5i v\u00e0 r\u00fat g\u1ecdn <\/i><\/span> "}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:14:52"},{"id":"1492","post_id":"797","mon_id":"0","chapter_id":"0","question":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","options":{"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":[[["1"],["626"]]],"list":[{"point":10,"width":50,"ques":"R\u00fat g\u1ecdn ph\u00e2n s\u1ed1 sau: <br\/> $\\dfrac{25^{28} + 25^{24} + .... + 25^4 + 1}{25^{30} + 25^{28} + ... + 25^2 + 1}$ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Quan s\u00e1t \u0111\u1ec1 b\u00e0i ta th\u1ea5y: \u1ede tr\u00ean t\u1eed l\u00e0 d\u00e3y c\u00e1c l\u0169y th\u1eeba c\u01a1 s\u1ed1 25, c\u00e1ch nhau 4 b\u1eadc; d\u01b0\u1edbi m\u1eabu l\u00e0 d\u00e3y c\u00e1c l\u0169y th\u1eeba c\u01a1 s\u1ed1 25, c\u00e1ch nhau 2 b\u1eadc <br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00e1ch c\u00e1c s\u1ed1 h\u1ea1ng \u1edf d\u01b0\u1edbi m\u1eabu th\u00e0nh 2 nh\u00f3m l\u0169y th\u1eeba trong \u0111\u00f3 m\u1ed7i nh\u00f3m g\u1ed3m c\u00e1c l\u0169y th\u1eeba c\u00e1ch nhau 4 b\u1eadc <br\/> <b> B\u01b0\u1edbc 2: <\/b> Bi\u1ebfn \u0111\u1ed5i l\u00e0m xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed chung \u1edf m\u1eabu <br\/> <b> B\u01b0\u1edbc 3: <\/b> R\u00fat g\u1ecdn nh\u1eefng nh\u00e2n t\u1eed chung \u1edf t\u1eed \u1edf t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1, 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*} & \\dfrac{25^{28} + 25^{24} + .... + 25^4 + 1}{(25^{30} + 25^{26} + ... + 25^{6} + 25^2) + (25^{28} + 25^{24} + ... + 25^4 + 1)} \\\\ &= \\dfrac{25^{28} + 25^{24} + ... + 25^4 + 1}{25^2 . (25^{28} + 25^{24} + ... + 25^{4} + 1) + (25^{28} + 25^{24} + ... + 25^{4} + 1)} \\\\ &= \\dfrac{25^{28} + 25^{24} + ... + 25^{4} + 1}{(25^{28} + 25^{24} + ... + 25^{4} + 1) . (25^2 + 1)} \\\\ &= \\dfrac{1}{25^2 + 1} \\\\ &= \\dfrac{1}{626} \\end{align*}$"}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:14:52"},{"id":"1493","post_id":"797","mon_id":"0","chapter_id":"0","question":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","options":{"time":14,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n \u0111\u00fang v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["60"],["72"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"Cho ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$, r\u00fat g\u1ecdn ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$ ta \u0111\u01b0\u1ee3c ph\u00e2n s\u1ed1 $\\dfrac{5}{6}$. N\u1ebfu th\u00eam 8 \u0111\u01a1n v\u1ecb v\u00e0o m\u1eabu s\u1ed1 b v\u00e0 gi\u1eef nguy\u00ean t\u1eed s\u1ed1 a th\u00ec ta \u0111\u01b0\u1ee3c m\u1ed9t ph\u00e2n s\u1ed1 m\u1edbi. R\u00fat g\u1ecdn ph\u00e2n s\u1ed1 m\u1edbi \u0111\u01b0\u1ee3c ph\u00e2n s\u1ed1 $\\dfrac{3}{4}$. T\u00ecm ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$ <br\/> \u0110\u00e1p \u00e1n l\u00e0: $\\dfrac{a}{b} $ = <div class=\"frac123\"><div class=\"ts\">_input_<\/div><div class=\"ms\">_input_<\/div><\/div>","hint":"","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> V\u00ec $\\dfrac{a}{b} = \\dfrac{5}{6}$ <br\/> N\u00ean ta t\u00ednh \u0111\u01b0\u1ee3c a theo b t\u1eeb \u0111\u1eb3ng th\u1ee9c tr\u00ean (1) <br\/> <b> B\u01b0\u1edbc 2: <\/b> V\u00ec $\\dfrac{a}{b + 8} = \\dfrac{3}{4}$ <br\/> N\u00ean ta t\u00ednh \u0111\u01b0\u1ee3c a theo b t\u1eeb \u0111\u1eb3ng th\u1ee9c tr\u00ean (2) <br\/> <b> B\u01b0\u1edbc 3: <\/b> Thay (1) v\u00e0o (2) ta t\u00ecm \u0111\u01b0\u1ee3c b <br\/> <b> B\u01b0\u1edbc 4: <\/b> Thay b tr\u1edf l\u1ea1i (1) ho\u1eb7c (2) \u0111\u1ec3 t\u00ecm a <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Theo \u0111\u1ec1 b\u00e0i ta c\u00f3: $\\dfrac{a}{b} = \\dfrac{5}{6}$ <br\/> $\\Rightarrow$ $a = \\dfrac{5b}{6}$ (1) <br\/> Khi c\u1ed9ng th\u00eam 8 v\u00e0o m\u1eabu s\u1ed1 v\u00e0 gi\u1eef nguy\u00ean t\u1eed s\u1ed1 ta \u0111\u01b0\u1ee3c: <br\/> $\\dfrac{a}{b + 8} = \\dfrac{3}{4}$ <br\/> $\\Rightarrow$ a . 4 = 3 . (b + 8) <br\/> 4a = 3b + 24 (2) <br\/> Thay a t\u1eeb (1) v\u00e0o (2) ta \u0111\u01b0\u1ee3c: <br\/> $\\begin{align*} 4.\\dfrac{5b}{6} & = 3b + 24 \\\\ \\dfrac{20b}{6}& = 3b + 24 \\\\ 20b &= 6 . (3b + 24) \\\\ 20b &= 18b + 144 \\\\ 2b &= 144 \\\\ b &= 72\\end{align*}$ <br\/> $\\Rightarrow$ $a = \\dfrac{5 . 72}{6} = \\dfrac{360}{6} = 60$ <br\/> <span class='basic_pink'> V\u1eady ph\u00e2n s\u1ed1 c\u1ea7n t\u00ecm l\u00e0: $\\dfrac{60}{72}$ <\/span> "}]}]},"correct":"","level":"3","hint":"","answer":"","type":"json","extra_type":"","time":"0","user_id":"0","test":"0","date":"2019-09-30 09:14:52"}]}