{"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>&nbsp;l&agrave; hai nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr&igrave;nh&nbsp;<span class=\"math-tex\">$x^2-3x-1=0$<\/span>. T&iacute;nh gi&aacute; tr\u1ecb bi\u1ec3u th\u1ee9c&nbsp;<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&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong>&nbsp;<span class=\"math-tex\">$3\\sqrt{13}$<\/span><\/span><\/p><p>Ta c&oacute;:&nbsp;<span class=\"math-tex\">$\\Delta=9+4=13&gt;0$<\/span>&nbsp;n&ecirc;n&nbsp;ph\u01b0\u01a1ng tr&igrave;nh lu&ocirc;n c&oacute;&nbsp;hai nghi\u1ec7m ph&acirc;n bi\u1ec7t&nbsp;<span class=\"math-tex\">$x_1=\\dfrac{3 + \\sqrt{13}}{2},x_2=\\dfrac{3- \\sqrt{13}}{2}$<\/span>.<\/p><p>Suy ra&nbsp;<span class=\"math-tex\">$x_1-x_2=\\sqrt{13}$<\/span>.<\/p><p>Theo \u0111\u1ecbnh l&iacute; Viet ta c&oacute;:&nbsp;<span class=\"math-tex\">$x_1+x_2=3,\\;x_1.x_2=-1$<\/span>.<\/p><p>Ta c&oacute;:&nbsp;<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 tr&igrave;nh&nbsp;<span class=\"math-tex\">$x^2-2(m-2)x+2m-5=0$<\/span>&nbsp;(v\u1edbi m l&agrave; tham s\u1ed1,&nbsp;<span class=\"math-tex\">$m\\ne3$<\/span>). Bi\u1ec3u th\u1ee9c li&ecirc;n h\u1ec7 gi\u1eefa&nbsp;<span class=\"math-tex\">$x_1,x_2$<\/span>&nbsp;kh&ocirc;ng ph\u1ee5 thu\u1ed9c v&agrave;o m l&agrave;:<\/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&nbsp;<span style=\"color:#16a085;\"><strong>D.<\/strong>&nbsp;<span class=\"math-tex\">$x_1+x_2-x_1x_2=1$<\/span><\/span><\/p><p>Ta c&oacute;:&nbsp;<span class=\"math-tex\">$\\Delta^\\prime=(m-3)^2\\ge0,\\forall m$<\/span>&nbsp;suy ra ph\u01b0\u01a1ng tr&igrave;nh c&oacute; hai nghi\u1ec7m&nbsp;<span class=\"math-tex\">$x_1,x_2$<\/span>&nbsp;v\u1edbi m\u1ecdi m&nbsp;<span class=\"math-tex\">$\\ne$<\/span>&nbsp;3.<\/p><p>&Aacute;p d\u1ee5ng h\u1ec7 th\u1ee9c Viet ta c&oacute;:&nbsp;<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 tr&igrave;nh ta \u0111\u01b0\u1ee3c:&nbsp;<span class=\"math-tex\">$x_1+x_2-x_1x_2=1$<\/span>.<\/p><p>V\u1eady&nbsp;bi\u1ec3u th\u1ee9c li&ecirc;n h\u1ec7 gi\u1eefa <span class=\"math-tex\">$x_1,x_2$<\/span>&nbsp;kh&ocirc;ng ph\u1ee5 thu\u1ed9c v&agrave;o tham s\u1ed1&nbsp;m l&agrave;:&nbsp;<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 c&oacute; t&iacute;ch b\u1eb1ng 2 v&agrave; t\u1ed5ng l\u1eadp ph\u01b0\u01a1ng b\u1eb1ng &ndash;9 th\u1ecfa m&atilde;n x &gt; y. T&iacute;nh <span class=\"math-tex\">$S = x + 2y$<\/span>.<\/p>","options":["<strong>A.<\/strong> 0","<strong>B.<\/strong> &ndash;5","<strong>C.<\/strong> &ndash;4","<strong>D.<\/strong> 3"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong>&nbsp;&ndash;5<\/span><\/p><p>V&igrave; x, y c&oacute; t&iacute;ch b\u1eb1ng 2 v&agrave; t\u1ed5ng l\u1eadp ph\u01b0\u01a1ng b\u1eb1ng &ndash;9 n&ecirc;n&nbsp;<\/p><p><span class=\"math-tex\">$\\begin{cases}xy=2\\\\x^3+y^3=-9\\end{cases}$<\/span>&nbsp;suy ra&nbsp;<span class=\"math-tex\">$\\begin{cases}xy=2\\$x+y)^3-3xy(x+y)=-9\\end{cases}$<\/span>&nbsp;hay&nbsp;<span class=\"math-tex\">$\\begin{cases}xy=2\\$x+y)^3-6(x+y)+9=0\\end{cases}$<\/span>.<\/p><p>\u0110\u1eb7t x + y = m, ph\u01b0\u01a1ng tr&igrave;nh th\u1ee9 hai tr\u1edf th&agrave;nh&nbsp;<span class=\"math-tex\">$m^3-6m+9=0$<\/span>&nbsp;hay&nbsp;<span class=\"math-tex\">$(m+3)(m^2-3m+3)=0$<\/span><\/p><p>&nbsp;&bull;&nbsp;<span class=\"math-tex\">$m^2-3m+3=0$<\/span>&nbsp;c&oacute;&nbsp;<span class=\"math-tex\">$\\Delta&lt;0$<\/span>&nbsp;n&ecirc;n ph\u01b0\u01a1ng tr&igrave;nh n&agrave;y v&ocirc; nghi\u1ec7m.<\/p><p>&nbsp;&bull;&nbsp;<span class=\"math-tex\">$m+3=0$<\/span>&nbsp;suy ra&nbsp;<span class=\"math-tex\">$m=-3$<\/span>.<\/p><p>Khi \u0111&oacute; h\u1ec7 ph\u01b0\u01a1ng tr&igrave;nh tr\u1edf th&agrave;nh&nbsp;<span class=\"math-tex\">$\\begin{cases}xy=2\\\\x+y=-3\\end{cases}$<\/span>.<\/p><p>Suy ra x, y l&agrave; nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr&igrave;nh&nbsp;<span class=\"math-tex\">$X^2+3X+2=0$<\/span>&nbsp;m&agrave; x &gt; y n&ecirc;n x =&nbsp;&ndash;1, y =&nbsp;&ndash;2.<\/p><p>Khi \u0111&oacute; S = (&ndash;1) + 2 . (&ndash;2) =&nbsp;&ndash;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}]}