{"common":{"save":0,"post_id":"7817","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7865","post_id":"7817","mon_id":"1159278","chapter_id":"1159327","question":"<p>So s&aacute;nh&nbsp;<span class=\"math-tex\">$\\dfrac{30-2\\sqrt{45}}{4}\\dots\\sqrt{17}$<\/span>.<\/p>","options":["<strong>A.<\/strong> &gt;","<strong>B.<\/strong> &lt;","<strong>C.<\/strong> ="],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong> &lt;.<\/span><\/p><p><span class=\"math-tex\">$\\dfrac{30-2\\sqrt{45}}{4}<\\dfrac{30-2\\sqrt{49}}{4}=\\dfrac{30-2.7}{4}=4=\\sqrt{16}<\\sqrt{17}$<\/span>.<\/p><p>Suy ra&nbsp;<span class=\"math-tex\">$\\dfrac{30-2\\sqrt{45}}{4}<\\sqrt{17}$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-17 01:17:57","option_type":"txt","len":0},{"id":"7867","post_id":"7817","mon_id":"1159278","chapter_id":"1159327","question":"<p>Trong c&aacute;c h\u1ec7 th\u1ee9c sau \u0111&acirc;y, h\u1ec7 th\u1ee9c n&agrave;o \u0111&uacute;ng v\u1edbi m\u1ecdi s\u1ed1 d\u01b0\u01a1ng a v&agrave; b?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\sqrt{a+b}=\\sqrt{a}+\\sqrt{b}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\sqrt{a+b}>\\sqrt{a}+\\sqrt{b}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\sqrt{a+b}<\\sqrt{a}+\\sqrt{b}$<\/span>","<strong>D.<\/strong> C\u1ea3 ba \u0111&aacute;p &aacute;n tr&ecirc;n"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;<span class=\"math-tex\">$\\sqrt{a+b}<\\sqrt{a}+\\sqrt{b}$<\/span>.<\/span><\/p><p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$(\\sqrt{a+b})^2=a+b$<\/span>.<\/p><p>L\u1ea1i c&oacute;&nbsp;<span class=\"math-tex\">$(\\sqrt{a}+\\sqrt{b})^2=a+b+2\\sqrt{ab}$<\/span>.<\/p><p>M&agrave;&nbsp;<span class=\"math-tex\">$a+b< a+b+2\\sqrt{ab}$<\/span>&nbsp;v\u1edbi m\u1ecdi a, b &gt; 0.<\/p><p>Suy ra \u0111&aacute;p &aacute;n <strong>A<\/strong> v&agrave; <strong>B<\/strong> \u0111\u1ec1u sai,&nbsp;\u0111&aacute;p &aacute;n <strong>C<\/strong> \u0111&uacute;ng.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-17 01:24:47","option_type":"math","len":0},{"id":"7869","post_id":"7817","mon_id":"1159278","chapter_id":"1159327","question":"<p>Cho bi\u1ec3u th\u1ee9c A =&nbsp;<span class=\"math-tex\">$\\sqrt[3]{2+\\sqrt{5}}+\\sqrt[3]{2-\\sqrt{5}}$<\/span>. T&iacute;nh B = A&nbsp;&ndash; 1.<\/p>","options":["<strong>A.<\/strong> B = 0","<strong>B.<\/strong> B = &ndash;1","<strong>C.<\/strong> B = 1","<strong>D.<\/strong> B = 2"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong> B = 0.<\/span><\/p><p>A&sup3; =&nbsp;<span class=\"math-tex\">$(\\sqrt[3]{2+\\sqrt{5}}+\\sqrt[3]{2-\\sqrt{5}})^3$<\/span><\/p><p>=&nbsp;<span class=\"math-tex\">$2+\\sqrt{5}+2-\\sqrt{5}+3\\sqrt[3]{(2+\\sqrt{5})(2-\\sqrt{5})}\\bigg(\\sqrt[3]{2+\\sqrt{5}}+\\sqrt[3]{2-\\sqrt{5}}\\bigg)$<\/span><\/p><p>=&nbsp;<span class=\"math-tex\">$4-3A$<\/span>.<\/p><p>Suy ra&nbsp;<span class=\"math-tex\">$A^3+3A-4=0$<\/span>.<\/p><p>Hay&nbsp;<span class=\"math-tex\">$(A-1)(A^2+A+4)=0$<\/span>.<\/p><p>M&agrave;&nbsp;<span class=\"math-tex\">$A^2+A+4=\\bigg(A+\\dfrac{1}{2}\\bigg)^2+\\dfrac{15}{4}>0$<\/span>&nbsp;v\u1edbi m\u1ecdi A&nbsp;&isin; R.<\/p><p>Suy ra A&nbsp;&ndash; 1 = 0 hay A = 1.<\/p><p>V\u1eady B = A&nbsp;&ndash; 1 = 1 &ndash; 1 = 0.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-10-17 01:33:33","option_type":"txt","len":1}]}