{"common":{"save":0,"post_id":"7808","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7554","post_id":"7808","mon_id":"1159278","chapter_id":"1159327","question":"<p>R&uacute;t g\u1ecdn bi\u1ec3u th\u1ee9c&nbsp;<span class=\"math-tex\">$B=\\sqrt{\\dfrac{5+2\\sqrt{6}}{5-2\\sqrt{6}}}+\\sqrt{\\dfrac{5-2\\sqrt{6}}{5+2\\sqrt{6}}}$<\/span>&nbsp;c&oacute; k\u1ebft&nbsp;qu\u1ea3 l&agrave;:<\/p>","options":["<strong>A.<\/strong> B = 14.","<strong>B.<\/strong> B = 10.","<strong>C.<\/strong> B = <span class=\"math-tex\">$2\\sqrt{6}$<\/span>.","<strong>D.<\/strong> B = <span class=\"math-tex\">$\\dfrac{\\sqrt{5}}{2}$<\/span>."],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong> B = 10.<\/span><\/p><p><span class=\"math-tex\">$B=\\sqrt{\\dfrac{5+2\\sqrt{6}}{5-2\\sqrt{6}}}+\\sqrt{\\dfrac{5-2\\sqrt{6}}{5+2\\sqrt{6}}}$<\/span><\/p><p><span class=\"math-tex\">$B=\\sqrt{\\dfrac{3+2\\sqrt{3}.\\sqrt{2}+2}{3-2\\sqrt{3}.\\sqrt{2}+2}}+\\sqrt{\\dfrac{3-2\\sqrt{3}.\\sqrt{2}+2}{3+2\\sqrt{3}.\\sqrt{2}+2}}$<\/span><\/p><p><span class=\"math-tex\">$B=\\sqrt{\\dfrac{(\\sqrt{3}+\\sqrt{2})^2}{(\\sqrt{3}-\\sqrt{2})^2}}+\\sqrt{\\dfrac{(\\sqrt{3}-\\sqrt{2})^2}{(\\sqrt{3}+\\sqrt{2})^2}}$<\/span><\/p><p><span class=\"math-tex\">$B=\\dfrac{\\sqrt{3}+\\sqrt{2}}{\\sqrt{3}-\\sqrt{2}}+\\dfrac{\\sqrt{3}-\\sqrt{2}}{\\sqrt{3}+\\sqrt{2}}$<\/span>&nbsp;<\/p><p><span class=\"math-tex\">$B=\\dfrac{(\\sqrt{3}+\\sqrt{2})^2+(\\sqrt{3}-\\sqrt{2})^2}{(\\sqrt{3}-\\sqrt{2})(\\sqrt{3}+\\sqrt{2})}$<\/span><\/p><p><span class=\"math-tex\">$B=\\dfrac{3+2\\sqrt{6}+2+3-2\\sqrt{6}+2}{3-2}=10$<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-11 01:06:38","option_type":"math","len":0},{"id":"7557","post_id":"7808","mon_id":"1159278","chapter_id":"1159327","question":"<p>Gi&aacute; tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c&nbsp;<span class=\"math-tex\">$(4-\\sqrt{15}).(\\sqrt{10}+\\sqrt{6}).\\sqrt{4+\\sqrt{15}}+1$<\/span> l&agrave;:<\/p>","options":["<strong>A.<\/strong> 3","<strong>B.<\/strong> <span class=\"math-tex\">$\\sqrt{10}+\\sqrt{6}+1$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\sqrt{10}-\\sqrt{6}+1$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\sqrt{5}-\\sqrt{3}+1$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;3<\/span><\/p><p><span class=\"math-tex\">$(4-\\sqrt{15}).(\\sqrt{10}+\\sqrt{6}).\\sqrt{4+\\sqrt{15}}+1$<\/span><\/p><p><span class=\"math-tex\">$=\\sqrt{4-\\sqrt{15}}.\\sqrt{4-\\sqrt{15}}.(\\sqrt{2}.\\sqrt{10}+\\sqrt{2}.\\sqrt{3}).\\sqrt{4+\\sqrt{15}}+1$<\/span><\/p><p><span class=\"math-tex\">$=\\sqrt{4-\\sqrt{15}}.\\sqrt{4+\\sqrt{15}}.\\sqrt{4-\\sqrt{15}}.\\sqrt{2}.(\\sqrt{5}+\\sqrt{3})+1$<\/span><\/p><p><span class=\"math-tex\">$=\\sqrt{(4-\\sqrt{15})(4+\\sqrt{15})}.\\sqrt{8-2\\sqrt{15}}.(\\sqrt{5}+\\sqrt{3})+1$<\/span><\/p><p><span class=\"math-tex\">$=\\sqrt{16-15}.\\sqrt{5-2\\sqrt{5}.\\sqrt{3}+3}.(\\sqrt{5}+\\sqrt{3})+1$<\/span><\/p><p><span class=\"math-tex\">$=\\sqrt{(\\sqrt{5}-\\sqrt{3})^2}.(\\sqrt{5}+\\sqrt{3})+1$<\/span><\/p><p><span class=\"math-tex\">$=(\\sqrt{5}-\\sqrt{3}).(\\sqrt{5}+\\sqrt{3})+1$<\/span><\/p><p><span class=\"math-tex\">$=(5-3)+1=3$<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-11 01:24:54","option_type":"math","len":0},{"id":"7558","post_id":"7808","mon_id":"1159278","chapter_id":"1159327","question":"<p>Cho&nbsp;<span class=\"math-tex\">$A=\\sqrt{3+\\sqrt{13+\\sqrt{48}}}$<\/span>. T&iacute;nh&nbsp;<span class=\"math-tex\">$A-\\sqrt{3}$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$1+\\sqrt{3}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$2\\sqrt{3}+1$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$1$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\sqrt{3}$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;<span class=\"math-tex\">$1$<\/span><\/span><\/p><p><span class=\"math-tex\">$A=\\sqrt{3+\\sqrt{13+\\sqrt{48}}}=\\sqrt{3+\\sqrt{13+\\sqrt{16}.\\sqrt{3}}}$<\/span><\/p><p><span class=\"math-tex\">$=\\sqrt{3+\\sqrt{13+4.\\sqrt{3}}}$<\/span>&nbsp;<span class=\"math-tex\">$=\\sqrt{3+\\sqrt{12+2.2\\sqrt{3}.1+1}}$<\/span><\/p><p><span class=\"math-tex\">$=\\sqrt{3+\\sqrt{(2\\sqrt{3}+1)^2}}$<\/span>&nbsp;<span class=\"math-tex\">$=\\sqrt{3+2\\sqrt{3}+1}$<\/span><\/p><p><span class=\"math-tex\">$=\\sqrt{(\\sqrt{3}+1)^2}=\\sqrt{3}+1$<\/span><\/p><p>V\u1eady&nbsp;<span class=\"math-tex\">$A-\\sqrt{3}=\\sqrt{3}+1-\\sqrt{3}=1$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-11 01:27:17","option_type":"math","len":0}]}