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HN
1
25 tháng 6 2016
A= \(\frac{6-\sqrt{6}}{\sqrt{6}-1}+\frac{6+\sqrt{6}}{\sqrt{6}}=\frac{\sqrt{6}\left(\sqrt{6}-1\right)}{\sqrt{6}-1}+\frac{\sqrt{6}\left(\sqrt{6}+1\right)}{\sqrt{6}}=\sqrt{6}+\sqrt{6}+1\)
= \(2\sqrt{6}+1\)
4 tháng 10 2019
\(=\frac{\sqrt{3}+\sqrt{2}-1}{2+\sqrt{6}}+\frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+1}\left(\frac{2\sqrt{3}+\sqrt{18}+2\sqrt{3}-\sqrt{18}}{4-6}\right)-\frac{1}{\sqrt{2}}.\)
\(=\frac{\sqrt{3}+\sqrt{2}-1}{2+\sqrt{6}}-\frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+1}.\left(2\sqrt{3}\right)-\frac{1}{\sqrt{2}}\)
\(=\frac{\sqrt{3}+\sqrt{2}-1}{2+\sqrt{6}}-\frac{2\sqrt{6}-6}{\sqrt{2}+1}-\frac{1}{\sqrt{2}}\)
16 tháng 7 2017
\(\frac{6-\sqrt{6}}{\sqrt{6}-1}+\frac{6+\sqrt{6}}{\sqrt{6}}\)\(=\frac{\sqrt{6}\left(\sqrt{6}-1\right)}{\sqrt{6}-1}+\frac{6}{\sqrt{6}}+\frac{\sqrt{6}}{\sqrt{6}}\)\(=\sqrt{6}+\frac{6}{\sqrt{6}}+1\)\(=\sqrt{6}\left(1+\frac{\sqrt{6}}{\sqrt{6}}\right)+1\)\(=\sqrt{6}\left(1+1\right)+1\)\(=\sqrt{6}.2+1\)
\(\frac{\sqrt{10}-\sqrt{2}}{\sqrt{5}-1}+\frac{2-\sqrt{2}}{\sqrt{2}-1}\)\(=\frac{\sqrt{2}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}+\frac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}\)\(=\sqrt{2}+\sqrt{2}=2\sqrt{2}\)
\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)\(=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20-2.3\sqrt{20}+9}}}\)\(=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(\sqrt{20}-3\right)^2}}}\)\(=\sqrt{\sqrt{5}-\sqrt{3-I\sqrt{20}-3I}}\)\(=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20}+3}}\)\(=\sqrt{\sqrt{5}-\sqrt{5-2\sqrt{5}+1}}\)\(=\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}\)\(=\sqrt{\sqrt{5}-I\sqrt{5}-1I}\)\(=\sqrt{\sqrt{5}-\sqrt{5}+1}\)\(=\sqrt{1}=1\)
14 tháng 11 2019
\(\frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}+\sqrt{5}}+\frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}-\sqrt{5}}\)
\(=\frac{\left(\sqrt{6}-\sqrt{5}\right)^2}{\left(\sqrt{6}+\sqrt{5}\right)\left(\sqrt{6}-\sqrt{5}\right)}+\frac{\left(\sqrt{6}+\sqrt{5}\right)^2}{\left(\sqrt{6}+\sqrt{5}\right)\left(\sqrt{6}-\sqrt{5}\right)}\)
\(=\frac{\left(\sqrt{6}-\sqrt{5}\right)^2+\left(\sqrt{6}+\sqrt{5}\right)^2}{\left(\sqrt{6}+\sqrt{5}\right)\left(\sqrt{6}-\sqrt{5}\right)}\)
\(=\frac{11-2\sqrt{30}+11+2\sqrt{30}}{\left(\sqrt{6}\right)^2-\left(\sqrt{5}\right)^2}\)
\(=\frac{22}{1}=22\)
14 tháng 11 2019
\(\frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}+\sqrt{5}}+\frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}-\sqrt{5}}\)
\(=\frac{\left(\sqrt{6}-\sqrt{5}\right)\left(\sqrt{6}-\sqrt{5}\right)+\left(\sqrt{6}+\sqrt{5}\right)\left(\sqrt{6}+\sqrt{5}\right)}{\left(\sqrt{6}+\sqrt{5}\right)\left(\sqrt{6}-\sqrt{5}\right)}\)
\(=\frac{\left(\sqrt{6}-\sqrt{5}\right)^2+\left(\sqrt{6}+\sqrt{5}\right)^2}{\sqrt{6}^2+\sqrt{5}^2}\)
\(=\sqrt{6}^2-2\sqrt{6}.\sqrt{5}+\sqrt{5}^2+\sqrt{6}^2+2\sqrt{6}.\sqrt{5}+\sqrt{5}^2\)
\(=6+5+6+5=22\)
YY
1 tháng 7 2015
\(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+1\right)=-5-10\sqrt{6}\)
Mình không chắc lắm
\(=\frac{\sqrt{6}\left(\sqrt{6}-1\right)}{\sqrt{6}-1}+\frac{\sqrt{6}\left(\sqrt{6}+1\right)}{\sqrt{6}}=\sqrt{6}+\sqrt{6}+1=2\sqrt{6}+1\)
\(\frac{6-\sqrt{6}}{\sqrt{6-1}}\)+ \(\frac{6+\sqrt{6}}{\sqrt{6}}\) = \(\frac{-\sqrt{30}+6\sqrt{5}}{5}\) + \(1+\sqrt{6}\) = \(\frac{\sqrt{6}\left(\sqrt{6-1}\right)}{\sqrt{6-1}}\) + \(\frac{\sqrt{6}\left(\sqrt{6-1}\right)}{\sqrt{6}}\) = \(\sqrt{6}+\sqrt{6}+1=2\sqrt{6+1}\)