Question

tính:

\(\left(\dfrac{3\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}-\dfrac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}\right).\dfrac{\sqrt{5}-3}{5-3\sqrt{10}}\)

Answer 1

Sửa đề: \(\left(\dfrac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}-\dfrac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}\right)\cdot\dfrac{\sqrt{5}-3}{5-3\sqrt{10}}\)

\(=\dfrac{7-2\sqrt{10}-7-2\sqrt{10}}{3}\cdot\dfrac{\sqrt{5}-3}{5-3\sqrt{10}}\)

\(=\dfrac{4\sqrt{10}}{3}\cdot\dfrac{3-\sqrt{5}}{\sqrt{5}\left(\sqrt{5}-3\sqrt{2}\right)}\)

\(=\dfrac{12\sqrt{10}-20\sqrt{2}}{3\sqrt{5}\left(\sqrt{5}-3\sqrt{2}\right)}\)