Question

\(\frac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}\)+\(\frac{8}{1-\sqrt{5}}\) (thực hiện phép tính)

Answer 1

Ta có: \(\frac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\frac{8}{1-\sqrt{5}}\)

\(=\frac{\sqrt{100}+\sqrt{40}}{\sqrt{5}+\sqrt{2}}+\frac{8}{1-\sqrt{5}}\)

\(=\frac{\sqrt{20}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{5}+\sqrt{2}}+\frac{8}{1-\sqrt{5}}\)

\(=\sqrt{20}+\frac{8}{1-\sqrt{5}}\)

\(=\frac{\sqrt{20}\left(1-\sqrt{5}\right)}{1-\sqrt{5}}+\frac{8}{1-\sqrt{5}}\)

\(=\frac{\sqrt{20}-10+8}{1-\sqrt{5}}\)

\(=\frac{\sqrt{20}-2}{1-\sqrt{5}}=\frac{2\left(\sqrt{5}-1\right)}{-\left(\sqrt{5}-1\right)}=\frac{2}{-1}=-2\)