Question

\(\frac{5+\sqrt{5}}{5-\sqrt{5}}\)+\(\frac{5-\sqrt{5}}{5+\sqrt{5}}\)Thu gọn

Answer 1

\(\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}\) 

\(=\frac{\left(5+\sqrt{5}\right)\left(5+\sqrt{5}\right)}{\left(5-\sqrt{5}\right)\left(5+\sqrt{5}\right)}\)\(+\frac{\left(5-\sqrt{5}\right)\left(5-\sqrt{5}\right)}{\left(5-\sqrt{5}\right)\left(5+\sqrt{5}\right)}\) 

\(=\frac{\left(5+\sqrt{5}\right)^2+\left(5-\sqrt{5}\right)^2}{25-5}\) 

\(=\frac{25+10\sqrt{5}+5+25-10\sqrt{5}+5}{20}\) 

\(=\frac{60}{20}=30\) 

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