{"common":{"save":0,"post_id":"7831","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7711","post_id":"7831","mon_id":"1159278","chapter_id":"1159282","question":"<p>Cho&nbsp;<span class=\"math-tex\">$x+y\\ge2$<\/span>. Ch\u1ecdn kh\u1eb3ng \u0111\u1ecbnh \u0111&uacute;ng.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$x^2+y^2\\ge2$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$x^2+y^2\\le2$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$x^2+y^2<2$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$x^2+y^2>2$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$x^2+y^2\\ge2$<\/span>.<\/span><\/p><p>T\u1eeb&nbsp;<span class=\"math-tex\">$x+y\\ge2$<\/span>, b&igrave;nh ph\u01b0\u01a1ng hai v\u1ebf (hai v\u1ebf \u0111\u1ec1u d\u01b0\u01a1ng) \u0111\u01b0\u1ee3c<\/p><p><span class=\"math-tex\">$x^2+2xy+y^2\\ge4$<\/span>&nbsp;(1).<\/p><p>T\u1eeb&nbsp;<span class=\"math-tex\">$(x-y)^2\\ge0$<\/span>&nbsp;suy ra&nbsp;<span class=\"math-tex\">$x^2-2xy+y^2\\ge0$<\/span>&nbsp;(2).<\/p><p>L\u1ea5y (1) c\u1ed9ng (2), v\u1ebf theo v\u1ebf, ta \u0111\u01b0\u1ee3c&nbsp;<span class=\"math-tex\">$2x^2 +2y^2\\ge4$<\/span>.<\/p><p>Chia hai v\u1ebf cho 2 ta \u0111\u01b0\u1ee3c&nbsp;<span class=\"math-tex\">$x^2+y^2\\ge2$<\/span>.<\/p><p>\u0110\u1eb3ng th\u1ee9c x\u1ea3y ra khi&nbsp;<span class=\"math-tex\">$\\begin{cases}x+y=2\\$x-y)^2=0\\end{cases}$<\/span>&nbsp;hay&nbsp;<span class=\"math-tex\">$\\begin{cases}x=1\\\\y=1\\end{cases}$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-13 03:16:30","option_type":"math","len":0},{"id":"7714","post_id":"7831","mon_id":"1159278","chapter_id":"1159282","question":"<p>Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr&igrave;nh&nbsp;<span class=\"math-tex\">$\\dfrac{x+1}{2017}+\\dfrac{x+3}{2019}+\\dfrac{x+5}{2021}+\\dfrac{x+7}{2023}+\\dfrac{x+9}{2025}=5$<\/span>&nbsp;l&agrave;<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$x=2016$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$x=2018$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$x=2020$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$x=2022$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$x=2016$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{x+1}{2017}+\\dfrac{x+3}{2019}+\\dfrac{x+5}{2021}+\\dfrac{x+7}{2023}+\\dfrac{x+9}{2025}=5$<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{x+1}{2017}-1+\\dfrac{x+3}{2019}-1+\\dfrac{x+5}{2021}1+\\dfrac{x+7}{2023}-1+\\dfrac{x+9}{2025}-1=0$<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{x+1-2017}{2017}+\\dfrac{x+3-2019}{2019}+\\dfrac{x+5-2021}{2021}+\\dfrac{x+7-2023}{2023}+\\dfrac{x+9-2025}{2025}=0$<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{x-2016}{2017}+\\dfrac{x-2016}{2019}+\\dfrac{x-2016}{2021}+\\dfrac{x-2016}{2023}+\\dfrac{x-2016}{2025}=0$<\/span><\/p><p><span class=\"math-tex\">$(x-2016)\\bigg(\\dfrac{1}{2017}+\\dfrac{1}{2019}+\\dfrac{1}{2021}+\\dfrac{1}{2023}+\\dfrac{1}{2025}\\bigg)=0$<\/span><\/p><p><span class=\"math-tex\">$x-2016=0$<\/span>&nbsp;(v&igrave;&nbsp;<span class=\"math-tex\">$\\dfrac{1}{2017}+\\dfrac{1}{2019}+\\dfrac{1}{2021}+\\dfrac{1}{2023}+\\dfrac{1}{2025}\\ne0$<\/span>)<\/p><p><span class=\"math-tex\">$x=2016$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-13 03:21:57","option_type":"math","len":0},{"id":"7717","post_id":"7831","mon_id":"1159278","chapter_id":"1159282","question":"<p>Ph\u01b0\u01a1ng tr&igrave;nh <span class=\"math-tex\">$x(x+1)(x-1)(x+2)=24$<\/span>&nbsp;c&oacute; nghi\u1ec7m l&agrave;<\/p>","options":["<strong>A.<\/strong> x = 1 ho\u1eb7c x = 3","<strong>B.<\/strong> x = 2 ho\u1eb7c x = &ndash;3","<strong>C.<\/strong> x = &ndash;1 ho\u1eb7c x = 3","<strong>D.<\/strong> x = 2 ho\u1eb7c x = 3"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<strong><span style=\"color:#16a085;\">B<\/span><span style=\"color:#16a085;\">.<\/span><\/strong><span style=\"color:#16a085;\">&nbsp;x = 2&nbsp;ho\u1eb7c x = &ndash;3.<\/span><\/p><p><span class=\"math-tex\">$x(x+1)(x-1)(x+2)=24$<\/span><\/p><p><span class=\"math-tex\">$(x^2+x)(x^2+x-2)-24=0$<\/span><\/p><p>\u0110\u1eb7t&nbsp;<span class=\"math-tex\">$t=x^2+x$<\/span>&nbsp;ta \u0111\u01b0\u1ee3c<\/p><p><span class=\"math-tex\">$t(t-2)-24=0$<\/span><\/p><p><span class=\"math-tex\">$t^2-2t-24=0$<\/span><\/p><p><span class=\"math-tex\">$t^2-2t+1-25=0$<\/span><\/p><p><span class=\"math-tex\">$(t-1)^2-25=0$<\/span><\/p><p><span class=\"math-tex\">$(t-1-5)(t-1+5)=0$<\/span><\/p><p><span class=\"math-tex\">$(t-6)(t+4)=0$<\/span><\/p><p><span class=\"math-tex\">$t=6$<\/span>&nbsp;ho\u1eb7c&nbsp;<span class=\"math-tex\">$t=-4$<\/span><\/p><p>V\u1edbi&nbsp;<span class=\"math-tex\">$t=6$<\/span>&nbsp;th&igrave;&nbsp;<span class=\"math-tex\">$x^2+x=6$<\/span>&nbsp;hay&nbsp;<span class=\"math-tex\">$x^2+x-6=0$<\/span>&nbsp;hay&nbsp;<span class=\"math-tex\">$(x-2)(x+3)=0$<\/span>&nbsp;hay<span style=\"color:#16a085;\">&nbsp;<span class=\"math-tex\">$x=2$<\/span>&nbsp;ho\u1eb7c&nbsp;<span class=\"math-tex\">$x=-3$<\/span><\/span>.<\/p><p>V\u1edbi&nbsp;<span class=\"math-tex\">$t=-4$<\/span>&nbsp;th&igrave;&nbsp;<span class=\"math-tex\">$x^2+x=-4$<\/span>&nbsp;hay&nbsp;<span class=\"math-tex\">$x^2+x+4=0$<\/span>&nbsp;hay&nbsp;<span class=\"math-tex\">$\\bigg(x+\\dfrac{1}{2}\\bigg)^2=-\\dfrac{15}{4}$<\/span>&nbsp;(v&ocirc; nghi\u1ec7m).<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-13 03:31:48","option_type":"txt","len":2}]}