{"common":{"save":0,"post_id":"6701","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7245","mon_id":"1158767","chapter_id":"1158893","post_id":"6701","question":"<p>T&igrave;m&nbsp;s\u1ed1 h\u1ea1ng kh&ocirc;ng ch\u1ee9a&nbsp;<span class=\"math-tex\">$x$<\/span> trong khai tri\u1ec3n nh\u1ecb th\u1ee9c Newton&nbsp;c\u1ee7a&nbsp;<span class=\"math-tex\">$\\bigg(2x^2-\\dfrac{1}{x^2}\\bigg)^4$<\/span><\/p>","options":["<b>A. <\/b>24","<b>B. <\/b>72","<b>C. <\/b>36","<b>D.<\/b> 35"],"correct":"1","level":"3","hint":"","answer":"<p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$\\bigg(2x^2-\\dfrac{1}{x^2}\\bigg)^4=$<\/span>&nbsp;<span class=\"math-tex\">$\\displaystyle\\sum_{k=0}^{4} C^k_4.(2x^2)^{4-k}.\\bigg(\\dfrac{-1}{x^2}\\bigg)^{k}=\\displaystyle\\sum_{k=0}^{4} C^k_4.2^{4-k}x^{8-4k}.(-1)^k$<\/span>.<\/p><p>S\u1ed1 h\u1ea1ng kh&ocirc;ng ch\u1ee9a&nbsp;<span class=\"math-tex\">$x$<\/span>&nbsp;trong khai tri\u1ec3n tr&ecirc;n \u1ee9ng v\u1edbi <span class=\"math-tex\">$8-4k=0\\Leftrightarrow k=2$<\/span>.<\/p><p>V\u1eady s\u1ed1&nbsp;h\u1ea1ng kh&ocirc;ng ch\u1ee9a&nbsp;<span class=\"math-tex\">$x$<\/span>&nbsp;trong khai tri\u1ec3n tr&ecirc;n&nbsp;l&agrave; <span class=\"math-tex\">$C_4^2.2^2.(-1)^2=24$<\/span>.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><b>A. <\/b>24<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-07-02 10:31:30","option_type":"txt","len":0},{"id":"7246","mon_id":"1158767","chapter_id":"1158893","post_id":"6701","question":"<p>Cho n l&agrave; s\u1ed1 nguy&ecirc;n d\u01b0\u01a1ng th\u1ecfa m&atilde;n <span class=\"math-tex\">$C_n^2=15-n$<\/span>. T&igrave;m s\u1ed1 h\u1ea1ng kh&ocirc;ng ch\u1ee9a x trong khai tri\u1ec3n&nbsp;<span class=\"math-tex\">$\\bigg(x+\\dfrac{2}{x^4}\\bigg)^n$<\/span><\/p>","options":["<strong>A. <\/strong>10","<strong>B. <\/strong>5 ","<strong>C. <\/strong>2","<strong>D. <\/strong>35"],"correct":"1","level":"3","hint":"","answer":"<p>\u0110i\u1ec1u ki\u1ec7n&nbsp;<span class=\"math-tex\">$n\\ge2,n\\in \\mathbb{N}^*$<\/span>&nbsp;(1).<\/p><p><span class=\"math-tex\">$C_n^2=15-n$<\/span>&nbsp;<span class=\"math-tex\">$\\Leftrightarrow n+\\dfrac{n(n-1)}{2}=15$<\/span>&nbsp;<span class=\"math-tex\">$\\Leftrightarrow n^2+n-30=0$<\/span>&nbsp;<span class=\"math-tex\">$\\Leftrightarrow n=5$<\/span>&nbsp;ho\u1eb7c&nbsp;<span class=\"math-tex\">$n=-6$<\/span>&nbsp;(lo\u1ea1i)<\/p><p>Suy ra n = 5.<\/p><p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$\\bigg(x+\\dfrac{2}{x^4}\\bigg)^5=$<\/span>&nbsp;<span class=\"math-tex\">$\\displaystyle\\sum_{k=0}^{5} C^k_5.x^{5-k}.\\bigg(\\dfrac{2}{x^4}\\bigg)^{k}=\\displaystyle\\sum_{k=0}^{5} C^k_5.2^k.x^{5-5k}$<\/span>.<\/p><p>S\u1ed1 h\u1ea1ng kh&ocirc;ng ch\u1ee9a&nbsp;<span class=\"math-tex\">$x$<\/span>&nbsp;trong khai tri\u1ec3n tr&ecirc;n \u1ee9ng v\u1edbi <span class=\"math-tex\">$5-5k=0\\Leftrightarrow k=1$<\/span>.<\/p><p>V\u1eady s\u1ed1&nbsp;h\u1ea1ng kh&ocirc;ng ch\u1ee9a&nbsp;<span class=\"math-tex\">$x$<\/span>&nbsp;trong khai tri\u1ec3n tr&ecirc;n&nbsp;l&agrave; <span class=\"math-tex\">$C_5^1.2^1=10$<\/span>.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.&nbsp;<\/strong>10<\/span><\/p>","type":"choose","extra_type":"shape1","user_id":"131","test":"0","date":"2023-07-03 13:00:18","option_type":"txt","len":0},{"id":"7249","mon_id":"1158767","chapter_id":"1158893","post_id":"6701","question":"<p>T&igrave;m s\u1ed1 h\u1ea1ng ch\u1ee9a&nbsp;<span class=\"math-tex\">$x^2$<\/span> trong khai tri\u1ec3n c\u1ee7a bi\u1ec3u th\u1ee9c <span class=\"math-tex\">$P(x)=(3+x^2)^n$<\/span>&nbsp;v\u1edbi n l&agrave; s\u1ed1 nguy&ecirc;n d\u01b0\u01a1ng th\u1ecfa m&atilde;n&nbsp;<span class=\"math-tex\">$C^2_n+\\dfrac{A^3_n}{n}=12$<\/span>.<\/p>","options":["<strong>A. <span class=\"math-tex\">$27x^2$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$4x^2$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$9x^2$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$108x^2$<\/span><\/strong>"],"correct":"4","level":"3","hint":"","answer":"<p>X&eacute;t&nbsp;<span class=\"math-tex\">$C^2_n+\\dfrac{A^3_n}{n}=12$<\/span>&nbsp;(1). \u0110i\u1ec1u ki\u1ec7n:&nbsp;<span class=\"math-tex\">$n\\in\\mathbb{Z},n\\ge3$<\/span>.<\/p><p>(1)&nbsp;<span class=\"math-tex\">$\\Leftrightarrow \\dfrac{n!}{2!(n-2)!}+ \\dfrac{n!}{n(n-3)!}=12$<\/span>&nbsp;<span class=\"math-tex\">$\\Leftrightarrow \\dfrac{n(n-1)}{2}+(n-2)(n-1)=12$<\/span><\/p><p><span class=\"math-tex\">$\\Leftrightarrow 3n^2-7n-20=0$<\/span>&nbsp;<span class=\"math-tex\">$\\Leftrightarrow n=4$<\/span>&nbsp;ho\u1eb7c&nbsp;<span class=\"math-tex\">$n=\\dfrac{-5}{3}$<\/span>&nbsp;(lo\u1ea1i).<\/p><p>V\u1edbi n = 4 ta c&oacute;&nbsp;<span class=\"math-tex\">$P(x)=(3+x^2)^4=$<\/span>&nbsp;<span class=\"math-tex\">$\\displaystyle\\sum_{k=0}^{4} C^k_4.3^{4-k}.x^{2k}$<\/span>.<\/p><p>S\u1ed1 h\u1ea1ng ch\u1ee9a&nbsp;<span class=\"math-tex\">$x^2$<\/span>&nbsp;trong khai tri\u1ec3n tr&ecirc;n \u1ee9ng v\u1edbi <span class=\"math-tex\">$2k=2\\Leftrightarrow k=1$<\/span>.<\/p><p>V\u1eady s\u1ed1&nbsp;h\u1ea1ng ch\u1ee9a&nbsp;<span class=\"math-tex\">$x^2$<\/span>&nbsp;trong khai tri\u1ec3n tr&ecirc;n&nbsp;l&agrave; <span class=\"math-tex\">$C_4^1.3^3.x^2=108x^2$<\/span>.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>D.&nbsp;<span class=\"math-tex\">$108x^2$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-07-03 13:18:44","option_type":"math","len":0}]}