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HomeLớp 10Toán lớp 10 - Sách Kết nối tri thứcBài 18. Phương trình quy về phương trình bậc haiBài tập trung bình
{"common":{"save":0,"post_id":"6466","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7126","mon_id":"1158767","chapter_id":"1158801","post_id":"6466","question":"<p>Tìm s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$(x-7)(\\sqrt{4x-9}-2x+5)=0$<\/span>.<\/p>","options":["<strong>A. <span class=\"math-tex\">$1$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$2$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$3$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$0$<\/span><\/strong>"],"correct":"2","level":"2","hint":"","answer":"<p>\u0110i\u1ec1u ki\u1ec7n <span class=\"math-tex\">$x\\ge\\dfrac{9}{4}$<\/span><\/p><p>Ta có: <span class=\"math-tex\">$(x-7)(\\sqrt{4x-9}-2x+5)=0$<\/span><\/p><p><span class=\"math-tex\">$\\Leftrightarrow x-7=0$<\/span> ho\u1eb7c <span class=\"math-tex\">$(\\sqrt{4x-9}-2x+5=0$<\/span>.<\/p><p>V\u1edbi <span class=\"math-tex\">$ x-7=0\\Leftrightarrow$<\/span> <span class=\"math-tex\">$x=7$<\/span> (th\u1ecfa \u0111i\u1ec1u ki\u1ec7n)<\/p><p>V\u1edbi <span class=\"math-tex\">$\\sqrt{4x-9}-2x+5=0\\Rightarrow2x^2-12x+17=0$<\/span> <span class=\"math-tex\">$\\Rightarrow x=\\dfrac{6-\\sqrt{2}}{2}$<\/span> ho\u1eb7c <span class=\"math-tex\">$x=\\dfrac{6+\\sqrt{2}}{2}$<\/span>.<\/p><p>Thay l\u1ea7n l\u01b0\u1ee3t hai giá tr\u1ecb này c\u1ee7a x vào ph\u01b0\u01a1ng trình \u0111ã cho, ta th\u1ea5y <span class=\"math-tex\">$x=\\dfrac{6+\\sqrt{2}}{2}$<\/span> th\u1ecfa mãn.<\/p><p>V\u1eady ph\u01b0\u01a1ng trình có hai nghi\u1ec7m là <span class=\"math-tex\">$x=7$<\/span> và <span class=\"math-tex\">$x=\\dfrac{6+\\sqrt{2}}{2}$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B. <span class=\"math-tex\">$2$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-03 09:45:53","option_type":"math","len":0},{"id":"7128","mon_id":"1158767","chapter_id":"1158801","post_id":"6466","question":"<p>Tìm s\u1ed1 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$(x-2)(\\sqrt{x^2-7x+10}-3x+1)=0$<\/span>.<\/p>","options":["<strong>A. <span class=\"math-tex\">$1$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$2$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$3$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$0$<\/span><\/strong>"],"correct":"2","level":"2","hint":"","answer":"<p>\u0110i\u1ec1u ki\u1ec7n <span class=\"math-tex\">$x^2-7x+10\\ge 0\\Leftrightarrow$<\/span><span class=\"math-tex\">$x\\ge 5$<\/span> ho\u1eb7c <span class=\"math-tex\">$x\\le2$<\/span><\/p><p>Ta có: <span class=\"math-tex\">$(x-2)(\\sqrt{x^2-7x+10}-3x+1)=0$<\/span>.<\/p><p><span class=\"math-tex\">$\\Leftrightarrow x-2=0$<\/span> ho\u1eb7c <span class=\"math-tex\">$\\sqrt{x^2-7x+10}-3x+1=0$<\/span>.<\/p><p>V\u1edbi <span class=\"math-tex\">$ x-2=0\\Leftrightarrow$<\/span> <span class=\"math-tex\">$x=2$<\/span> (th\u1ecfa \u0111i\u1ec1u ki\u1ec7n)<\/p><p>V\u1edbi <span class=\"math-tex\">$\\sqrt{x^2-7x+10}-3x+1=0\\Rightarrow$<\/span> <span class=\"math-tex\">$8x^2+x-9=0$<\/span> <span class=\"math-tex\">$\\Rightarrow x=1$<\/span> ho\u1eb7c <span class=\"math-tex\">$x=\\dfrac{-9}{8}$<\/span>.<\/p><p>Thay l\u1ea7n l\u01b0\u1ee3t hai giá tr\u1ecb này c\u1ee7a x vào ph\u01b0\u01a1ng trình \u0111ã cho, ta th\u1ea5y <span class=\"math-tex\">$x=1$<\/span> th\u1ecfa mãn.<\/p><p>V\u1eady ph\u01b0\u01a1ng trình có hai nghi\u1ec7m là <span class=\"math-tex\">$x=2$<\/span> và <span class=\"math-tex\">$x=1$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B. <span class=\"math-tex\">$2$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-03 09:53:51","option_type":"math","len":0},{"id":"7130","mon_id":"1158767","chapter_id":"1158801","post_id":"6466","question":"<p>T\u1ed5ng các nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$\\sqrt{-x^2+8x-5}=x$<\/span> là:<\/p>","options":["<strong>A. <span class=\"math-tex\">$-2$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$2$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$4$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$-4$<\/span><\/strong>"],"correct":"3","level":"2","hint":"","answer":"<p>\u0110i\u1ec1u ki\u1ec7n <span class=\"math-tex\">$-x^2+8x-5\\ge 0\\Leftrightarrow$<\/span> <span class=\"math-tex\">$4-\\sqrt{11}\\le x\\le 4+\\sqrt{11}$<\/span>.<\/p><p>Ta có: <span class=\"math-tex\">$\\sqrt{-x^2+8x-5}=x$<\/span><\/p><p><span class=\"math-tex\">$\\Leftrightarrow \\begin{cases}x\\ge0\\\\-x^2+8x-5=x^2\\end{cases}$<\/span> <span class=\"math-tex\">$\\Leftrightarrow \\begin{cases}x\\ge0\\\\2x^2-8x+5=0\\end{cases}$<\/span> <span class=\"math-tex\">$\\Leftrightarrow x=\\dfrac{4\\pm\\sqrt{6}}{2}$<\/span> (th\u1ecfa \u0111i\u1ec1u ki\u1ec7n)<\/p><p>Ph\u01b0\u01a1ng trình có hai nghi\u1ec7m <span class=\"math-tex\">$x=\\dfrac{4+\\sqrt{6}}{2}$<\/span> và <span class=\"math-tex\">$ x=\\dfrac{4+\\sqrt{6}}{2}$<\/span>. <\/p><p>T\u1ed5ng c\u1ee7a chúng là <span class=\"math-tex\">$\\dfrac{4+\\sqrt{6}}{2}$<\/span><span class=\"math-tex\">$+\\dfrac{4+\\sqrt{6}}{2}=4$<\/span><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C. <span class=\"math-tex\">$4$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-03 10:02:07","option_type":"math","len":0}]}