Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
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{"common":{"save":0,"post_id":"6464","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6959","mon_id":"1158767","chapter_id":"1158801","post_id":"6464","question":"<p>Gi\u1ea3i h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng trình sau <span class=\"math-tex\">$\\begin{cases}2x^2-7x+5>0\\\\-x^2+2x+3\\geq0\\end{cases}$<\/span>.<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$[-1;1)\\cup\\bigg(\\dfrac{5}{2};3\\bigg]$<\/span>","<strong>B. <\/strong><span class=\"math-tex\">$\\bigg(\\dfrac{5}{2};3\\bigg)$<\/span>","<strong>C. <\/strong><span class=\"math-tex\">$(-1;1)$<\/span>","<strong>D. <\/strong><span class=\"math-tex\">$(-1;1)\\cup\\bigg(\\dfrac{5}{2};3\\bigg)$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>B\u1ea5t ph\u01b0\u01a1ng trình th\u1ee9 nh\u1ea5t có t\u1eadp nghi\u1ec7m là <span class=\"math-tex\">$S_1=(-\\infty;1)\\cup \\bigg(\\dfrac{5}{2};+\\infty\\bigg)$<\/span>.<\/p><p>B\u1ea5t ph\u01b0\u01a1ng trình th\u1ee9 hai có t\u1eadp nghi\u1ec7m là <span class=\"math-tex\">$S_2=[-1;3]$<\/span>.<\/p><p>T\u1eadp nghi\u1ec7m c\u1ee7a h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng trình là: <span class=\"math-tex\">$\u200b\u200bS=S_1\\cap S_2=$<\/span><span class=\"math-tex\">$[-1;1)\\cup\\bigg(\\dfrac{5}{2};3\\bigg]$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A. <\/strong><span class=\"math-tex\">$[-1;1)\\cup\\bigg(\\dfrac{5}{2};3\\bigg]$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-05-31 02:35:31","option_type":"math","len":0},{"id":"6961","mon_id":"1158767","chapter_id":"1158801","post_id":"6464","question":"<p>Tìm các giá tr\u1ecb c\u1ee7a m \u0111\u1ec3 b\u1ea5t ph\u01b0\u01a1ng trình sau vô nghi\u1ec7m: <span class=\"math-tex\">$(m-2)x^2+2(m+1)x+2m>0$<\/span>.<\/p>","options":["<strong>A. <span class=\"math-tex\">$m<3+\\sqrt{10}$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$m\\le 3-\\sqrt{10}$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$m\\ge 3-\\sqrt{10}$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$m\\le 3+\\sqrt{10}$<\/span><\/strong>"],"correct":"2","level":"3","hint":"","answer":"<p>\u0110\u1eb7t <span class=\"math-tex\">$f(x)=(m-2)x^2+2(m+1)x+2m$<\/span>.<\/p><p>\u0110\u1ec3 b\u1ea5t ph\u01b0\u01a1ng trình vô nghi\u1ec7m khi và ch\u1ec9 khi <span class=\"math-tex\">$f(x)\\le0,\\forall x$<\/span>. <br \/>V\u1edbi <span class=\"math-tex\">$m=2$<\/span> ta có <span class=\"math-tex\">$f(x)=6x+4$<\/span> khi \u0111ó <span class=\"math-tex\">$f(x)$<\/span> nh\u1eadn c\u1ea3 các giá tr\u1ecb d\u01b0\u01a1ng. Nên giá tr\u1ecb <span class=\"math-tex\">$m=2$<\/span> không th\u1ecfa mãn \u0111i\u1ec1u ki\u1ec7n<br \/>V\u1edbi <span class=\"math-tex\">$m\\ne2$<\/span> ta có:<\/p><p><span class=\"math-tex\">$f(x)\\le0,\\forall x\\in\\mathbb{R}\\Leftrightarrow$<\/span><span class=\"math-tex\">$\\begin{cases}m-2<0\\\\-m^2+6m+1\\le0\\end{cases}$<\/span><span class=\"math-tex\">$\\Leftrightarrow\\begin{cases}m<2\\\\m\\le3-\\sqrt{10}\\space\\space ho\u1eb7c\\space\\space m\\ge3+\\sqrt{10}\\end{cases}$<\/span><span class=\"math-tex\">$\\Leftrightarrow m\\le3-\\sqrt{10}$<\/span>.<\/p><p>V\u1eady b\u1ea5t ph\u01b0\u01a1ng trình vô nghi\u1ec7m khi và ch\u1ec9 khi <span class=\"math-tex\">$ m\\le3-\\sqrt{10}$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B. <span class=\"math-tex\">$m\\le 3-\\sqrt{10}$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-05-31 03:03:24","option_type":"math","len":0},{"id":"6964","mon_id":"1158767","chapter_id":"1158801","post_id":"6464","question":"<p>V\u1edbi nh\u1eefng giá tr\u1ecb nào c\u1ee7a m thì \u0111a th\u1ee9c <span class=\"math-tex\">$f(x)=(2-m)x^2-2x+1$<\/span> luôn d\u01b0\u01a1ng v\u1edbi m\u1ecdi x thu\u1ed9c \u211d.<\/p>","options":["<strong>A. <span class=\"math-tex\">$m>1$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$m\\ge1$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$m<1$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$m\\le 1$<\/span><\/strong>"],"correct":"3","level":"3","hint":"","answer":"<p>V\u1edbi <span class=\"math-tex\">$m=2$<\/span> ta có <span class=\"math-tex\">$f(x)=-2x+1$<\/span> khi \u0111ó <span class=\"math-tex\">$f(x)$<\/span> nh\u1eadn c\u1ea3 các giá tr\u1ecb âm. Nên giá tr\u1ecb <span class=\"math-tex\">$m=2$<\/span> không th\u1ecfa mãn \u0111i\u1ec1u ki\u1ec7n.<\/p><p>V\u1edbi <span class=\"math-tex\">$m\\ne2$<\/span> ta có <span class=\"math-tex\">$f(x)>0,\\forall x\\in\\mathbb{R}\\Leftrightarrow$<\/span><span class=\"math-tex\">$\\begin{cases}2-m>0\\\\m-1<0\\end{cases}$<\/span><span class=\"math-tex\">$\\Leftrightarrow\\begin{cases}m<2\\\\m<1\\end{cases}$<\/span><span class=\"math-tex\">$\\Leftrightarrow m<1$<\/span>.<\/p><p>V\u1eady khi <span class=\"math-tex\">$ m<1$<\/span> thì <span class=\"math-tex\">$f(x)>0,\\forall x\\in\\mathbb{R}$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C. <span class=\"math-tex\">$m<1$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-05-31 03:31:47","option_type":"math","len":0}]}