Question

Tính :\(\frac{2}{\sqrt{5}+1}+\frac{2}{\sqrt{5}-1}\)

Answer 1

\(\frac{2}{\sqrt{5}+1}+\frac{2}{\sqrt{5}-1}\)

\(=\frac{2\left(\sqrt{5}-1\right)}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}+\frac{2\left(\sqrt{5}+1\right)}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}\)

\(=\frac{2\left(\sqrt{5}-1\right)+2\left(\sqrt{5}+1\right)}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}\)

\(=\frac{2\left(\sqrt{5}-1+\sqrt{5}+1\right)}{5-1}\)

\(=\frac{4\sqrt{5}}{4}=\sqrt{5}\)