{"common":{"save":0,"post_id":"7098","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5378","post_id":"7098","mon_id":"1158924","chapter_id":"1159168","question":"<p>Bi\u1ec3u th\u1ee9c <span class=\"math-tex\">$\\sqrt{x\\sqrt{x\\sqrt{x\\sqrt{x\\sqrt{x}}}}}$<\/span> v\u1edbi x > 0 \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng l\u0169y th\u1eeba v\u1edbi s\u1ed1 m\u0169 h\u1eefu t\u1ec9 là:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\huge x^{^{\\frac{31}{32}}}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\huge x^{^{\\frac{15}{8}}}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\huge x^{^{\\frac{7}{8}}}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\huge x^{^{\\frac{15}{16}}}$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$\\huge x^{^{\\frac{31}{32}}}$<\/span><\/span><\/p><p><span class=\"math-tex\">$\\sqrt{x\\sqrt{x\\sqrt{x\\sqrt{x\\sqrt{x}}}}}\\n=x^{^{\\frac{1}{2}}}.x^{^{\\frac{1}{2}.\\frac{1}{2}}}\\n.x^{^{\\frac{1}{2}.\\frac{1}{2}.\\frac{1}{2}}} \\n.x^{^{\\frac{1}{2}.\\frac{1}{2}.\\frac{1}{2}.\\frac{1}{2}}}\\n.x^{^{\\frac{1}{2}.\\frac{1}{2}.\\frac{1}{2}.\\frac{1}{2}.\\frac{1}{2}}}$<\/span><\/p><p><span class=\"math-tex\">$=x^{^{\\frac{1}{2}}}.x^{^{\\frac{1}{4}}}.x^{^{\\frac{1}{8}}} .x^{^{\\frac{1}{16}}}.x^{^{\\frac{1}{32}}}$<\/span><\/p><p><span class=\"math-tex\">$=x^{^{\\frac{31}{32}}}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-31 03:32:31","option_type":"math","len":0},{"id":"5381","post_id":"7098","mon_id":"1158924","chapter_id":"1159168","question":"<p>K\u1ebft qu\u1ea3 <span class=\"math-tex\">$a^{^\\frac{5}{2}}$<\/span> v\u1edbi a > 0 là bi\u1ec3u th\u1ee9c rút g\u1ecdn c\u1ee7a phép tính<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\sqrt{a}.\\sqrt[5]{a}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{\\sqrt[3]{a^7}.\\sqrt{a}}{\\sqrt[3]{a}}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$a^5.\\sqrt{a}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{\\sqrt[4]{a^5}}{\\sqrt{a}}$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{\\sqrt[3]{a^7}.\\sqrt{a}}{\\sqrt[3]{a}}$<\/span><\/span><\/p><p>Ta có: <\/p><p><span class=\"math-tex\">$\\dfrac{\\sqrt[3]{a^7}.\\sqrt{a}}{\\sqrt[3]{a}}=a^{^\\frac{7}{3}}.a^{^\\frac{1}{2}}:a^{^\\frac{1}{3}}\\n=a^{^{\\frac{7}{3}+\\frac{1}{2}-\\frac{1}{3}}}\\n=a^{^\\frac{5}{2}}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-31 03:43:17","option_type":"math","len":0},{"id":"5382","post_id":"7098","mon_id":"1158924","chapter_id":"1159168","question":"<p>Bi\u1ebft <span class=\"math-tex\">$\\dfrac{x^{a^2}}{x^{b^2}}=x^{16}$<\/span> v\u1edbi x > 1 và a + b = 8. Giá tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c M = a – b là:<\/p>","options":["<strong>A.<\/strong> M = 18","<strong>B.<\/strong> M = 14","<strong>C.<\/strong> M = 2","<strong>D.<\/strong> M = 6"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> M = 2<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{x^{a^2}}{x^{b^2}}=x^{16}\\Leftrightarrow x^{a^2-b^2}=x^{16}\\Leftrightarrow a^2-b^2=16\\n$<\/span> <\/p><p><span class=\"math-tex\">$\\Leftrightarrow (a-b)(a+b)=16$<\/span><\/p><p><span class=\"math-tex\">$\\Leftrightarrow (a-b).8=16$<\/span> (vì a + b = 8)<\/p><p><span class=\"math-tex\">$\\Leftrightarrow a-b=2$<\/span><\/p><p>V\u1eady M = 2<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-03-31 03:48:00","option_type":"txt","len":0}]}
