\(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}\)
\(=\dfrac{\left(10+2\sqrt{10}\right)\left(\sqrt{5}-\sqrt{2}\right)}{3}+\dfrac{8\left(1+\sqrt{5}\right)}{-4}\)
\(=\dfrac{10\sqrt{5}-10\sqrt{2}+2\sqrt{50}-2\sqrt{20}}{3}+\left[-2\left(1+\sqrt{5}\right)\right]\)
\(=\dfrac{10\sqrt{5}-10\sqrt{2}+10\sqrt{2}-2\sqrt{20}}{3}+\left[-2-2\sqrt{5}\right]\)
\(=\dfrac{10\sqrt{5}-4\sqrt{5}}{3}-2-2\sqrt{5}\)
\(=\dfrac{6\sqrt{5}}{3}-2-2\sqrt{5}\)
\(=2\sqrt{5}-2-2\sqrt{5}\)
\(=-2\)
\(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}=\dfrac{2\sqrt{5}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{5}+\sqrt{2}}+\dfrac{8\left(1+\sqrt{5}\right)}{\left(1+\sqrt{5}\right)\left(1-\sqrt{5}\right)}=2\sqrt{5}+\dfrac{8\left(1+\sqrt{5}\right)}{-4}=2\sqrt{5}-2\left(1+\sqrt{5}\right)=2\sqrt{5}-2-2\sqrt{5}=-2\)
Vậy \(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}=-2\)
