Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
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{"common":{"save":0,"post_id":"7950","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8740","post_id":"7950","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\">$x^2-3x-1=0$<\/span>. Tính giá tr\u1ecb bi\u1ec3u th\u1ee9c <span class=\"math-tex\">$C=\\bigg|\\dfrac{1}{x_1^2}-\\dfrac{1}{x_2^2}\\bigg|$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{3\\sqrt{13}}{2}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$3\\sqrt{13}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$2\\sqrt{13}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$3\\sqrt{23}$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$3\\sqrt{13}$<\/span><\/span><\/p><p>Ta có: <span class=\"math-tex\">$\\Delta=9+4=13>0$<\/span> nên ph\u01b0\u01a1ng trình luôn có hai nghi\u1ec7m phân bi\u1ec7t <span class=\"math-tex\">$x_1=\\dfrac{3 + \\sqrt{13}}{2},x_2=\\dfrac{3- \\sqrt{13}}{2}$<\/span>.<\/p><p>Suy ra <span class=\"math-tex\">$x_1-x_2=\\sqrt{13}$<\/span>.<\/p><p>Theo \u0111\u1ecbnh lí Viet ta có: <span class=\"math-tex\">$x_1+x_2=3,\\;x_1.x_2=-1$<\/span>.<\/p><p>Ta có: <span class=\"math-tex\">$C=\\bigg|\\dfrac{1}{x_1^2}-\\dfrac{1}{x_2^2}\\bigg| =\\dfrac{|(x_1-x_2)(x_1+x_2)|}{x_1^2x_2^2}$<\/span><span class=\"math-tex\">$=\\dfrac{|\\sqrt{13}.3|}{(-1)^2}=3\\sqrt{13}$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-21 09:25:07","option_type":"math","len":0},{"id":"8759","post_id":"7950","mon_id":"1159278","chapter_id":"1159330","question":"<p>Cho ph\u01b0\u01a1ng trình <span class=\"math-tex\">$x^2-2(m-2)x+2m-5=0$<\/span> (v\u1edbi m là tham s\u1ed1, <span class=\"math-tex\">$m\\ne3$<\/span>). Bi\u1ec3u th\u1ee9c liên h\u1ec7 gi\u1eefa <span class=\"math-tex\">$x_1,x_2$<\/span> không ph\u1ee5 thu\u1ed9c vào m là:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$x_1+x_2+x_1x_2=1$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$x_1+x_2-x_1x_2=-1$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$x_1+x_2+x_1x_2=-1$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$x_1+x_2-x_1x_2=1$<\/span>"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$x_1+x_2-x_1x_2=1$<\/span><\/span><\/p><p>Ta có: <span class=\"math-tex\">$\\Delta^\\prime=(m-3)^2\\ge0,\\forall m$<\/span> suy ra ph\u01b0\u01a1ng trình có hai nghi\u1ec7m <span class=\"math-tex\">$x_1,x_2$<\/span> v\u1edbi m\u1ecdi m <span class=\"math-tex\">$\\ne$<\/span> 3.<\/p><p>Áp d\u1ee5ng h\u1ec7 th\u1ee9c Viet ta có: <span class=\"math-tex\">$\\begin{cases}x_1+x_2=2m-4\\\\x_1.x_2=2m-5\\end{cases}$<\/span><\/p><p>Tr\u1eeb t\u1eebng v\u1ebf hai ph\u01b0\u01a1ng trình ta \u0111\u01b0\u1ee3c: <span class=\"math-tex\">$x_1+x_2-x_1x_2=1$<\/span>.<\/p><p>V\u1eady bi\u1ec3u th\u1ee9c liên h\u1ec7 gi\u1eefa <span class=\"math-tex\">$x_1,x_2$<\/span> không ph\u1ee5 thu\u1ed9c vào tham s\u1ed1 m là: <span class=\"math-tex\">$x_1+x_2-x_1x_2=1$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-22 07:49:33","option_type":"math","len":0},{"id":"8761","post_id":"7950","mon_id":"1159278","chapter_id":"1159330","question":"<p>Bi\u1ebft x, y có tích b\u1eb1ng 2 và t\u1ed5ng l\u1eadp ph\u01b0\u01a1ng b\u1eb1ng –9 th\u1ecfa mãn x > y. Tính <span class=\"math-tex\">$S = x + 2y$<\/span>.<\/p>","options":["<strong>A.<\/strong> 0","<strong>B.<\/strong> –5","<strong>C.<\/strong> –4","<strong>D.<\/strong> 3"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> –5<\/span><\/p><p>Vì x, y có tích b\u1eb1ng 2 và t\u1ed5ng l\u1eadp ph\u01b0\u01a1ng b\u1eb1ng –9 nên <\/p><p><span class=\"math-tex\">$\\begin{cases}xy=2\\\\x^3+y^3=-9\\end{cases}$<\/span> suy ra <span class=\"math-tex\">$\\begin{cases}xy=2\\$x+y)^3-3xy(x+y)=-9\\end{cases}$<\/span> hay <span class=\"math-tex\">$\\begin{cases}xy=2\\$x+y)^3-6(x+y)+9=0\\end{cases}$<\/span>.<\/p><p>\u0110\u1eb7t x + y = m, ph\u01b0\u01a1ng trình th\u1ee9 hai tr\u1edf thành <span class=\"math-tex\">$m^3-6m+9=0$<\/span> hay <span class=\"math-tex\">$(m+3)(m^2-3m+3)=0$<\/span><\/p><p> • <span class=\"math-tex\">$m^2-3m+3=0$<\/span> có <span class=\"math-tex\">$\\Delta<0$<\/span> nên ph\u01b0\u01a1ng trình này vô nghi\u1ec7m.<\/p><p> • <span class=\"math-tex\">$m+3=0$<\/span> suy ra <span class=\"math-tex\">$m=-3$<\/span>.<\/p><p>Khi \u0111ó h\u1ec7 ph\u01b0\u01a1ng trình tr\u1edf thành <span class=\"math-tex\">$\\begin{cases}xy=2\\\\x+y=-3\\end{cases}$<\/span>.<\/p><p>Suy ra x, y là nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$X^2+3X+2=0$<\/span> mà x > y nên x = –1, y = –2.<\/p><p>Khi \u0111ó S = (–1) + 2 . (–2) = –5.<\/p>","type":"choose","extra_type":"shape2","time":"0","user_id":"127","test":"0","date":"2024-11-22 07:51:51","option_type":"txt","len":0}]}