Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
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{"common":{"save":0,"post_id":"7949","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8730","post_id":"7949","mon_id":"1159278","chapter_id":"1159330","question":"<p>Gi\u1ea3 s\u1eed <span class=\"math-tex\">$x_1,x_2$<\/span> là hai nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$x^2-5x+3=0$<\/span>. Tính <span class=\"math-tex\">$A=x_1^2+x_2^2-1$<\/span>.<\/p>","options":["<strong>A.<\/strong> 19","<strong>B.<\/strong> 18","<strong>C.<\/strong> 20","<strong>D.<\/strong> 17"],"correct":"2","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> 18<\/span><\/p><p>Ta có: <span class=\"math-tex\">$\\Delta=13>0$<\/span> nên ph\u01b0\u01a1ng trình có hai nghi\u1ec7m phân bi\u1ec7t <span class=\"math-tex\">$x_1,x_2$<\/span>.<\/p><p>Áp d\u1ee5ng h\u1ec7 th\u1ee9c Viet ta có <span class=\"math-tex\">$\\begin{cases}x_1+x_2=5\\\\x_1x_2=3\\end{cases} $<\/span>.<\/p><p>Ta có: <span class=\"math-tex\">$A=x_1^2+x_2^2-1=(x_1+x_2)^2-2x_1x_2-1=5^2-2.3-1=18$<\/span>.<\/p>","type":"choose","extra_type":"shape1","time":"0","user_id":"127","test":"0","date":"2024-11-21 08:27:25","option_type":"txt","len":0},{"id":"8731","post_id":"7949","mon_id":"1159278","chapter_id":"1159330","question":"<p>Gi\u1ea3 s\u1eed <span class=\"math-tex\">$x_1,x_2$<\/span> là hai nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$x^2-5x-1=0$<\/span>. Tính <span class=\"math-tex\">$A=x_1^2+x_2^2-x_1-x_2$<\/span>.<\/p>","options":["<strong>A.<\/strong> 20","<strong>B.<\/strong> 18","<strong>C.<\/strong> 22","<strong>D.<\/strong> 24"],"correct":"3","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> 22<\/span><\/p><p>Ta có: <span class=\"math-tex\">$\\Delta=29>0$<\/span> nên ph\u01b0\u01a1ng trình có hai nghi\u1ec7m phân bi\u1ec7t <span class=\"math-tex\">$x_1,x_2$<\/span>.<\/p><p>Áp d\u1ee5ng h\u1ec7 th\u1ee9c Viet ta có <span class=\"math-tex\">$\\begin{cases}x_1+x_2=5\\\\x_1x_2=-1\\end{cases} $<\/span>.<\/p><p>Ta có: <span class=\"math-tex\">$A=x_1^2+x_2^2-x_1-x_2=(x_1+x_2)^2-2x_1x_2-(x_1+x_2)=5^2-2.(-1)-5=22$<\/span>.<\/p>","type":"choose","extra_type":"shape2","time":"0","user_id":"127","test":"0","date":"2024-11-21 08:29:09","option_type":"txt","len":0},{"id":"8732","post_id":"7949","mon_id":"1159278","chapter_id":"1159330","question":"<p>Gi\u1ea3 s\u1eed <span class=\"math-tex\">$x_1,x_2$<\/span> là hai nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$-3x^2-5x-2=0$<\/span>. Tính <span class=\"math-tex\">$A=x_1+x_2+\\dfrac{1}{x_1}+\\dfrac{1}{x_2}$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{25}{3}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$-\\dfrac{25}{3}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{25}{6}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$-\\dfrac{25}{6}$<\/span>"],"correct":"4","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$-\\dfrac{25}{6}$<\/span><\/span><\/p><p>Ta có: <span class=\"math-tex\">$\\Delta=1>0$<\/span> nên ph\u01b0\u01a1ng trình có hai nghi\u1ec7m phân bi\u1ec7t <span class=\"math-tex\">$x_1,x_2$<\/span>.<\/p><p>Áp d\u1ee5ng h\u1ec7 th\u1ee9c Viet ta có <span class=\"math-tex\">$\\begin{cases}x_1+x_2=\\dfrac{-5}{3}\\\\x_1x_2=\\dfrac{2}{3}\\end{cases} $<\/span>.<\/p><p>Ta có: <span class=\"math-tex\">$A=x_1+x_2+\\dfrac{1}{x_1}+\\dfrac{1}{x_2}=x_1+x_2+\\dfrac{x_1+x_2}{x_1x_2}$<\/span> <span class=\"math-tex\">$=\\dfrac{-5}{3}+\\dfrac{-5}{3}.\\dfrac{3}{2}=\\dfrac{-25}{6}$<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-21 08:31:39","option_type":"math","len":0}]}