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HomeLớp 10Toán lớp 10 - Sách Kết nối tri thứcBài 18. Phương trình quy về phương trình bậc haiBài tập nâng cao
{"common":{"save":0,"post_id":"6467","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7143","mon_id":"1158767","chapter_id":"1158801","post_id":"6467","question":"<p>Tìm t\u1ea5t c\u1ea3 các giá tr\u1ecb nguyên d\u01b0\u01a1ng c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 ph\u01b0\u01a1ng trình (\u1ea9n x) <span class=\"math-tex\">$\\sqrt{x-2}=4-m$<\/span> có nghi\u1ec7m.<\/p>","options":["<strong>A. <\/strong>{0; 1; 2; 3; 4}","<strong>B. <\/strong>{2; 3; 4}","<strong>C. <\/strong>{1; 2; 3; 4}","<strong>D. <\/strong>{1; 2}"],"correct":"3","level":"3","hint":"","answer":"<p>\u0110i\u1ec1u ki\u1ec7n: <span class=\"math-tex\">$x-2\\ge0\\Leftrightarrow$<\/span> <span class=\"math-tex\">$x\\ge 2$<\/span>.<\/p><p>+ N\u1ebfu <span class=\"math-tex\">$4-m<0\\Leftrightarrow$<\/span> <span class=\"math-tex\">$m>4$<\/span> thì ph\u01b0\u01a1ng trình \u0111ã cho vô nghi\u1ec7m.<\/p><p>+ N\u1ebfu <span class=\"math-tex\">$4-m\\ge0\\Leftrightarrow$<\/span> <span class=\"math-tex\">$m\\le4$<\/span> thì ta có:<\/p><p><span class=\"math-tex\">$\\sqrt{x-2}=4-m$<\/span> <span class=\"math-tex\">$\\Leftrightarrow x=(4-m)^2+2\\ge2$<\/span> (th\u1ecfa \u0111i\u1ec1u ki\u1ec7n)<\/p><p>Suy ra ph\u01b0\u01a1ng trình có nghi\u1ec7m là <span class=\"math-tex\">$ x=(4-m)^2+2$<\/span>.<\/p><p>Vì <span class=\"math-tex\">$m\\le4$<\/span> nên các giá tr\u1ecb nguyên d\u01b0\u01a1ng c\u1ee7a tham s\u1ed1 m \u0111\u1ec3 ph\u01b0\u01a1ng trình có nghi\u1ec7m là m ∈ {1; 2; 3; 4}.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C. <\/strong>{1; 2; 3; 4}<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-04 03:21:07","option_type":"txt","len":2},{"id":"7144","mon_id":"1158767","chapter_id":"1158801","post_id":"6467","question":"<p>Tìm m \u0111\u1ec3 ph\u01b0\u01a1ng trình <span class=\"math-tex\">$(x^2+5x+4)\\sqrt{x-m}=0$<\/span> có \u0111úng hai nghi\u1ec7m phân bi\u1ec7t.<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$-4 \\le m < -1$<\/span>","<strong>B. <\/strong><span class=\"math-tex\">$-4< m <-1$<\/span>","<strong>C. <\/strong><span class=\"math-tex\">$-4\\le m\\le-1$<\/span>","<strong>D. <\/strong><span class=\"math-tex\">$-4< m\\le-1$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>\u0110i\u1ec1u ki\u1ec7n: <span class=\"math-tex\">$x-m\\ge0\\Leftrightarrow$<\/span> <span class=\"math-tex\">$x\\ge m$<\/span>.<\/p><p>Ta có: <span class=\"math-tex\">$(x^2+5x+4)\\sqrt{x-m}=0$<\/span> <span class=\"math-tex\">$\\Leftrightarrow $<\/span> <span class=\"math-tex\">$x^2+5x+4=0$<\/span> ho\u1eb7c <span class=\"math-tex\">$\\sqrt{x-m}=0$<\/span>.<\/p><p>V\u1edbi <span class=\"math-tex\">$x^2+5x+4=0$<\/span> <span class=\"math-tex\">$\\Leftrightarrow $<\/span> <span class=\"math-tex\">$x=-1$<\/span> ho\u1eb7c <span class=\"math-tex\">$x=-4$<\/span>.<\/p><p>V\u1edbi <span class=\"math-tex\">$\\sqrt{x-m}=0$<\/span> <span class=\"math-tex\">$\\Leftrightarrow $<\/span> <span class=\"math-tex\">$x=m$<\/span>.<\/p><p>\u0110\u1ec3 ph\u01b0\u01a1ng trình có \u0111úng hai nghi\u1ec7m phân bi\u1ec7t khi và ch\u1ec9 khi <span class=\"math-tex\">$-4 \\le m < -1$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A. <\/strong><span class=\"math-tex\">$-4 \\le m < -1$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-04 03:28:26","option_type":"math","len":0},{"id":"7145","mon_id":"1158767","chapter_id":"1158801","post_id":"6467","question":"<p>Tìm m \u0111\u1ec3 ph\u01b0\u01a1ng trình <span class=\"math-tex\">$(x^2+x)\\sqrt{x-m}=0$<\/span> ch\u1ec9 có m\u1ed9t nghi\u1ec7m.<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$m\\le0$<\/span>","<strong>B. <\/strong><span class=\"math-tex\">$m<0$<\/span>","<strong>C. <\/strong><span class=\"math-tex\">$m>0$<\/span>","<strong>D. <\/strong><span class=\"math-tex\">$m\\ge 0$<\/span>"],"correct":"4","level":"3","hint":"","answer":"<p>\u0110i\u1ec1u ki\u1ec7n: <span class=\"math-tex\">$x-m\\ge0\\Leftrightarrow$<\/span> <span class=\"math-tex\">$x\\ge m$<\/span>.<\/p><p>Ta có: <span class=\"math-tex\">$(x^2+x)\\sqrt{x-m}=0$<\/span> <span class=\"math-tex\">$\\Leftrightarrow $<\/span> <span class=\"math-tex\">$x^2+x=0$<\/span> ho\u1eb7c <span class=\"math-tex\">$\\sqrt{x-m}=0$<\/span>.<\/p><p>V\u1edbi <span class=\"math-tex\">$x^2+x=0$<\/span> <span class=\"math-tex\">$\\Leftrightarrow $<\/span> <span class=\"math-tex\">$x=-1$<\/span> ho\u1eb7c <span class=\"math-tex\">$x=0$<\/span>.<\/p><p>V\u1edbi <span class=\"math-tex\">$\\sqrt{x-m}=0$<\/span> <span class=\"math-tex\">$\\Leftrightarrow $<\/span> <span class=\"math-tex\">$x=m$<\/span> (th\u1ecfa \u0111i\u1ec1u ki\u1ec7n).<\/p><p>Ph\u01b0\u01a1ng trình luôn có nghi\u1ec7m <span class=\"math-tex\">$x=m$<\/span>. \u0110\u1ec3 ph\u01b0\u01a1ng trình có nghi\u1ec7m duy nh\u1ea5t thì <span class=\"math-tex\">$m\\ge0$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D. <\/strong><span class=\"math-tex\">$m\\ge 0$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-04 03:57:12","option_type":"math","len":0}]}