Question

Найти значение выражения

Answer 1

$\frac{1}{\sqrt[6]{9-4\sqrt5}}-\frac{1}{\sqrt[6]{9+4\sqrt5}}=\frac{1}{\sqrt[6]{(\sqrt5-2)^2}}-\frac{1}{\sqrt[6]{(\sqrt5+2)^2}}=\frac{1}{\sqrt[3]{\sqrt5-2}}-\frac{1}{\sqrt[3]{\sqrt5+2}}=\\\\\\=\frac{\sqrt[3]{\sqrt5+2}-\sqrt[3]{\sqrt5-2}}{\sqrt[3]{(\sqrt5-2)(\sqrt5+2)}}=\frac{\sqrt[3]{\sqrt5+2}-\sqrt[3]{\sqrt5-2} }{\sqrt[3]{5-4}}=\sqrt[3]{\sqrt5+2}-\sqrt[3]{\sqrt5-2}$