{"common":{"save":0,"post_id":"7781","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7233","post_id":"7781","mon_id":"1159278","chapter_id":"1159282","question":"<p>Ph\u01b0\u01a1ng tr&igrave;nh <span class=\"math-tex\">$(2x^2+x-6)^2+3(2x^2+x-3)=9$<\/span> c&oacute; s\u1ed1&nbsp;nghi\u1ec7m l&agrave;<\/p>","options":["<strong>A.<\/strong> 1","<strong>B.<\/strong> 2","<strong>C.<\/strong> 4","<strong>D.<\/strong> 3"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;4<\/span><\/p><p>\u0110\u1eb7t&nbsp;<span class=\"math-tex\">$t=2x^2+x-6$<\/span>. Khi \u0111&oacute;&nbsp;<span class=\"math-tex\">$2x^2+x-3=(2x^2+x-6)+3=t+3$<\/span><\/p><p>Khi \u0111&oacute; ph\u01b0\u01a1ng tr&igrave;nh&nbsp;<span class=\"math-tex\">$(2x^2+x-6)^2+3(2x^2+x-3)=9$<\/span>&nbsp;tr\u1edf th&agrave;nh<\/p><p><span class=\"math-tex\">$t^2+3(t+3)=9$<\/span><\/p><p><span class=\"math-tex\">$t^2+3t=0$<\/span><\/p><p><span class=\"math-tex\">$t(t+3)=0$<\/span><\/p><p>Suy ra t = 0 ho\u1eb7c t =&nbsp;&ndash;3.<\/p><p>&diams; V\u1edbi&nbsp;t = 0 th&igrave;&nbsp;<span class=\"math-tex\">$2x^2+x-6=0$<\/span>&nbsp;hay&nbsp;<span class=\"math-tex\">$(x+2)\\bigg(x-\\dfrac{3}{2}\\bigg)=0$<\/span><\/p><p>&nbsp;Suy ra x =&nbsp;&ndash;2 ho\u1eb7c x =&nbsp;<span class=\"math-tex\">$\\dfrac{3}{2}$<\/span>.<\/p><p>&diams; V\u1edbi&nbsp;t = &ndash;3&nbsp;th&igrave;&nbsp;<span class=\"math-tex\">$2x^2+x-6=-3$<\/span>&nbsp;hay&nbsp;<span class=\"math-tex\">$2x^2+x-3=0$<\/span>&nbsp;hay&nbsp;<span class=\"math-tex\">$(x-1)\\bigg(x+\\dfrac{3}{2}\\bigg)=0$<\/span><\/p><p>&nbsp;Suy ra x =&nbsp;1 ho\u1eb7c x =&nbsp;<span class=\"math-tex\">$-\\dfrac{3}{2}$<\/span>.<\/p><p>V\u1eady ph\u01b0\u01a1ng tr&igrave;nh d&atilde; cho c&oacute; 4 nghi\u1ec7m l&agrave;&nbsp;x =&nbsp;&ndash;2; x =&nbsp;<span class=\"math-tex\">$\\dfrac{3}{2}$<\/span>;&nbsp;x =&nbsp;1;&nbsp;x =&nbsp;<span class=\"math-tex\">$-\\dfrac{3}{2}$<\/span>.<\/p>","type":"choose","extra_type":"flower","time":"0","user_id":"127","test":"0","date":"2024-10-04 03:08:29","option_type":"txt","len":0},{"id":"7234","post_id":"7781","mon_id":"1159278","chapter_id":"1159282","question":"<p>Ph\u01b0\u01a1ng tr&igrave;nh&nbsp;<span class=\"math-tex\">$\\dfrac{x-1}{x+2}-\\dfrac{x}{x-2}=\\dfrac{5x-2}{4-x^2}$<\/span>&nbsp;c&oacute; nghi\u1ec7m l&agrave;<\/p>","options":["<strong>A.<\/strong> x &isin; <span class=\"math-tex\">$\\varnothing$<\/span>","<strong>B.<\/strong> x &isin; \u211d","<strong>C.<\/strong> Nghi\u1ec7m \u0111&uacute;ng v\u1edbi m\u1ecdi x &ne; &plusmn;2","<strong>D.<\/strong> x = 1; x = 0"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;Nghi\u1ec7m \u0111&uacute;ng v\u1edbi m\u1ecdi x&nbsp;&ne;&nbsp;&plusmn;2<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{x-1}{x+2}-\\dfrac{x}{x-2}=\\dfrac{5x-2}{4-x^2}$<\/span>&nbsp;(\u0110kx\u0111: x &ne; 2; x&nbsp;&ne;&nbsp;&ndash;2)<\/p><p><span class=\"math-tex\">$\\dfrac{x-1}{x+2}-\\dfrac{x}{x-2}=\\dfrac{-5x+2}{(x-2)(x+2)}$<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{(x-1)(x-2)}{(x-2)(x+2)}-\\dfrac{x(x+2)}{(x-2)(x+2)}=\\dfrac{-5x+2}{(x-2)(x+2)}$<\/span><\/p><p><span class=\"math-tex\">$x^2-3x+2-x^2-2x=-5x+2$<\/span><\/p><p><span class=\"math-tex\">$0x=0$<\/span>&nbsp;(lu&ocirc;n \u0111&uacute;ng)<\/p><p>K\u1ebft h\u1ee3p \u0110KX\u0110 ta c&oacute; ph\u01b0\u01a1ng tr&igrave;nh nghi\u1ec7m \u0111&uacute;ng v\u1edbi m\u1ecdi&nbsp;x &ne; 2; x&nbsp;&ne;&nbsp;&ndash;2.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-04 03:15:01","option_type":"math","len":0},{"id":"7308","post_id":"7781","mon_id":"1159278","chapter_id":"1159282","question":"<p>Ph\u01b0\u01a1ng tr&igrave;nh&nbsp;<span class=\"math-tex\">$\\dfrac{1}{x^2+4x+3}+\\dfrac{1}{x^2+8x+15}+\\dfrac{1}{x^2+12x+35}+\\dfrac{1}{x^2+16x+63}=\\dfrac{1}{5}$<\/span> c&oacute;&nbsp;nghi\u1ec7m l&agrave;<\/p>","options":["<strong>A.<\/strong> V&ocirc; nghi\u1ec7m.","<strong>B.<\/strong> V&ocirc; s\u1ed1 nghi\u1ec7m.","<strong>C.<\/strong> x = 1 ho\u1eb7c x = &ndash;11.","<strong>D.<\/strong> x = 1 ho\u1eb7c x = &ndash;11 ho\u1eb7c x = 11."],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;x = 1 ho\u1eb7c x =&nbsp;&ndash;11.<\/span><\/p><p>Ta c&oacute;:&nbsp;<span class=\"math-tex\">$x^2+4x+3=x^2+x+3x+3=(x+1)(x+3)$<\/span><\/p><p><span class=\"math-tex\">$x^2+8x+15=x^2+5x+3x+15=(x+5)(x+3)$<\/span><\/p><p><span class=\"math-tex\">$x^2+12x+35=x^2+5x+7x+15=(x+5)(x+7)$<\/span><\/p><p><span class=\"math-tex\">$x^2+16x+63=x^2+7x+9x+63=(x+7)(x+9)$<\/span><\/p><p>Khi \u0111&oacute; ph\u01b0\u01a1ng tr&igrave;nh \u0111&atilde; cho tr\u1edf th&agrave;nh<\/p><p><span class=\"math-tex\">$\\dfrac{1}{(x+1)(x+3)}+\\dfrac{1}{(x+3)(x+5)}+\\dfrac{1}{(x+5)(x+7)}+\\dfrac{1}{(x+7)(x+9)}=\\dfrac{1}{5}$<\/span><\/p><p>(\u0110kx\u0111: x &ne; &ndash;1; x&nbsp;&ne;&nbsp;&ndash;3; x&nbsp;&ne;&nbsp;&ndash;5; x&nbsp;&ne;&nbsp;&ndash;7; x&nbsp;&ne;&nbsp;&ndash;9)<\/p><p><span class=\"math-tex\">$\\dfrac{2}{(x+1)(x+3)}+\\dfrac{2}{(x+3)(x+5)}+\\dfrac{2}{(x+5)(x+7)}+\\dfrac{2}{(x+7)(x+9)}=\\dfrac{2}{5}$<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{1}{x+1}-\\dfrac{1}{x+3}+\\dfrac{1}{x+3}-\\dfrac{1}{x+5}+\\dfrac{1}{x+5}-\\dfrac{1}{x+7}+\\dfrac{1}{x+7}-\\dfrac{1}{x+9}=\\dfrac{2}{5}$<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{1}{x+1}-\\dfrac{1}{x+9}=\\dfrac{2}{5}$<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{5(x+9)}{5(x+1)(x+9)}-\\dfrac{5(x+1)}{5(x+1)(x+9)}=\\dfrac{2(x+1)(x+9)}{5(x+1)(x+9)}$<\/span><\/p><p><span class=\"math-tex\">$5x+45-5x-5=2x^2+20x+18$<\/span><\/p><p><span class=\"math-tex\">$x^2+10x-11=0$<\/span><\/p><p><span class=\"math-tex\">$x^2-x+11x-11=0$<\/span><\/p><p><span class=\"math-tex\">$(x-1)(x+11)=0$<\/span>&nbsp;suy ra <strong><span style=\"color:#16a085;\">x = 1 ho\u1eb7c x =&nbsp;&ndash;11&nbsp;<\/span><\/strong>(th\u1ecfa \u0111kx\u0111).<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-06 01:15:32","option_type":"txt","len":2}]}