{"common":{"save":0,"post_id":"6463","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6934","mon_id":"1158767","chapter_id":"1158801","post_id":"6463","question":"<p>S\u1ed1 nghi\u1ec7m nguyên c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng trình <span class=\"math-tex\">$2x^2+3x<2$<\/span> là:<\/p>","options":["<strong>A.<\/strong> 2 .","<strong>B.<\/strong> 3 . ","<strong>C.<\/strong> 4 .","<strong>D. <\/strong>5 ."],"correct":"1","level":"2","hint":"","answer":"<p>Ta có: <span class=\"math-tex\">$2x^2+3x<2\\Leftrightarrow 2x^2+3x-2<0\\Leftrightarrow-2< x <\\dfrac{1}{2}$<\/span>.<\/p><p>T\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng trình là: <span class=\"math-tex\">$S=\\bigg(-2;\\dfrac{1}{2}\\bigg)$<\/span>.<\/p><p>Do \u0111ó b\u1ea5t ph\u01b0\u01a1ng trình có 2 nghi\u1ec7m nguyên là <span class=\"math-tex\">$-1;0$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> 2 .<\/span><\/p>","type":"choose","extra_type":"shape1","user_id":"131","test":"0","date":"2023-05-30 09:47:45","option_type":"txt","len":0},{"id":"6935","mon_id":"1158767","chapter_id":"1158801","post_id":"6463","question":"<p>S\u1ed1 nghi\u1ec7m nguyên c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng trình <span class=\"math-tex\">$-x^2+16\\ge 0$<\/span> là:<\/p>","options":["<strong>A.<\/strong> 6.","<strong>B.<\/strong> 9.","<strong>C.<\/strong> 8.","<strong>D.<\/strong> 7."],"correct":"2","level":"2","hint":"","answer":"<p>Ta có: <span class=\"math-tex\">$-x^2+16\\ge 0\\Leftrightarrow -4\\le x \\le4$<\/span>.<\/p><p>T\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng trình là: <span class=\"math-tex\">$S=[-4;4]$<\/span>.<\/p><p>Do \u0111ó b\u1ea5t ph\u01b0\u01a1ng trình có <strong>9<\/strong> nghi\u1ec7m nguyên là <span class=\"math-tex\">$-4;-3;-2;-2;-1;0;1;2;3;4$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> 9.<\/span><\/p>","type":"choose","extra_type":"shape2","user_id":"131","test":"0","date":"2023-05-30 09:53:28","option_type":"txt","len":0},{"id":"6938","mon_id":"1158767","chapter_id":"1158801","post_id":"6463","question":"<p>Mi\u1ec1n nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng trình <span class=\"math-tex\">$\\dfrac{x-1}{x^2+x+1}<\\dfrac{x+1}{x^2-x+1}$<\/span> là:<\/p>","options":["<strong>A. <\/strong>∅","<strong>B. <span class=\"math-tex\">$\\bigg( -\\infty;-\\dfrac{1}{3}\\bigg)\\cup \\bigg(\\dfrac{1}{3} ;+\\infty\\bigg)$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$\\bigg( -\\dfrac{1}{3}; \\dfrac{1}{3} \\bigg)$<\/span><\/strong>","<strong>D. <\/strong><span class=\"math-tex\">$\\mathbb{R}$<\/span>"],"correct":"4","level":"2","hint":"","answer":"<p>Nh\u1eadn xét <span class=\"math-tex\">$x^2+x+1>0,\\forall x\\in \\mathbb{R}$<\/span>; <span class=\"math-tex\">$x^2-x+1>0,\\forall x\\in \\mathbb{R}$<\/span>.<\/p><p><span class=\"math-tex\">$\\dfrac{x-1}{x^2+x+1}<\\dfrac{x+1}{x^2-x+1}\\Leftrightarrow$<\/span><span class=\"math-tex\">$(x-1)(x^2-x+1)<(x+1)(x^2+x+1)$<\/span><\/p><p><span class=\"math-tex\">$\\Leftrightarrow x^3-2x^2+2x-1< x^3+2x^2+2x+1$<\/span><\/p><p><span class=\"math-tex\">$\\Leftrightarrow 4x^2+2>0\\Leftrightarrow x\\in\\mathbb{R}$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D. <\/strong><span class=\"math-tex\">$\\mathbb{R}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-05-30 10:07:25","option_type":"math","len":0}]}
