{"common":{"save":0,"post_id":"6700","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7234","mon_id":"1158767","chapter_id":"1158893","post_id":"6700","question":"<p>T&igrave;m h\u1ec7 s\u1ed1 c\u1ee7a s\u1ed1 h\u1ea1ng ch\u1ee9a&nbsp;<span class=\"math-tex\">$x^2$<\/span> trong khai tri\u1ec3n nh\u1ecb th\u1ee9c Newton&nbsp;c\u1ee7a&nbsp;<span class=\"math-tex\">$\\bigg(\\dfrac{1}{x}+x^3\\bigg)^6$<\/span><\/p>","options":["<strong>A. <\/strong>30","<strong>B. <\/strong>15","<strong>C. <\/strong>6","<strong>D. <\/strong>12"],"correct":"2","level":"2","hint":"","answer":"<p>Ta c&oacute; <span class=\"math-tex\">$\\bigg(\\dfrac{1}{x}+x^3\\bigg)^6=\\displaystyle\\sum_{k=0}^{6} C^k_6.\\bigg(\\dfrac{1}{x}\\bigg)^{6-k}.(x^3)^k=\\displaystyle\\sum_{k=0}^{6} C^k_6x^{4k-6}$<\/span>.<\/p><p>S\u1ed1 h\u1ea1ng ch\u1ee9a <span class=\"math-tex\">$x^2$<\/span>&nbsp;trong khai tri\u1ec3n tr&ecirc;n \u1ee9ng v\u1edbi <span class=\"math-tex\">$4k-6=2\\Leftrightarrow k=2$<\/span>.<\/p><p>V\u1eady h\u1ec7 s\u1ed1 c\u1ee7a s\u1ed1 h\u1ea1ng ch\u1ee9a&nbsp;<span class=\"math-tex\">$x^2$<\/span> trong khai tri\u1ec3n tr&ecirc;n&nbsp;l&agrave; <span class=\"math-tex\">$C_6^2=15$<\/span>.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.&nbsp;<\/strong>15<\/span><\/p>","type":"choose","extra_type":"shape1","user_id":"131","test":"0","date":"2023-07-02 09:55:01","option_type":"txt","len":0},{"id":"7235","mon_id":"1158767","chapter_id":"1158893","post_id":"6700","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\">$\\bigg(\\dfrac{1}{x}+x^4\\bigg)^5$<\/span><\/p>","options":["<strong>A. <\/strong>1","<strong>B. <\/strong>5","<strong>C. <\/strong>6","<strong>D. <\/strong>4"],"correct":"2","level":"2","hint":"","answer":"<p>Ta c&oacute; <span class=\"math-tex\">$\\bigg(\\dfrac{1}{x}+x^4\\bigg)^5=\\displaystyle\\sum_{k=0}^{5} C^k_5.\\bigg(\\dfrac{1}{x}\\bigg)^{5-k}.(x^4)^k=\\displaystyle\\sum_{k=0}^{5} C^k_5x^{5k-5}$<\/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\">$5k-5=0\\Leftrightarrow k=1$<\/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\">$C_5^1=5$<\/span>.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.&nbsp;<\/strong>5<\/span><\/p>","type":"choose","extra_type":"shape2","user_id":"131","test":"0","date":"2023-07-02 09:55:34","option_type":"txt","len":0},{"id":"7237","mon_id":"1158767","chapter_id":"1158893","post_id":"6700","question":"<p>T&igrave;m s\u1ed1 h\u1ea1ng ch\u1ee9a&nbsp;<span class=\"math-tex\">$x^5$<\/span> trong khai tri\u1ec3n nh\u1ecb th\u1ee9c Newton&nbsp;c\u1ee7a&nbsp;<span class=\"math-tex\">$(2x-1)^5$<\/span><\/p>","options":["<strong>A. <span class=\"math-tex\">$672x^2$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$-32x^5$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$32x^5$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$-672x^5$<\/span><\/strong>"],"correct":"3","level":"2","hint":"","answer":"<p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$(2x-1)^5=$<\/span>&nbsp;<span class=\"math-tex\">$\\displaystyle\\sum_{k=0}^{5} C^k_5.(2x)^{5-k}.1^k=\\displaystyle\\sum_{k=0}^{5} C^k_5.2^{5-k}x^{5-k}$<\/span>.<\/p><p>S\u1ed1 h\u1ea1ng ch\u1ee9a <span class=\"math-tex\">$x^5$<\/span>&nbsp;trong khai tri\u1ec3n tr&ecirc;n \u1ee9ng v\u1edbi <span class=\"math-tex\">$5-k=5\\Leftrightarrow k=0$<\/span>.<\/p><p>V\u1eady s\u1ed1 h\u1ea1ng ch\u1ee9a <span class=\"math-tex\">$x^5$<\/span>&nbsp;trong khai tri\u1ec3n tr&ecirc;n&nbsp;l&agrave; <span class=\"math-tex\">$C_5^0.2^5.x^5=32x^5$<\/span>.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.&nbsp;<span class=\"math-tex\">$32x^5$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-07-02 10:00:58","option_type":"math","len":0}]}