Question

Làm ơn giúp em với ạ

Answer 1

\(B=\dfrac{2\sqrt{2}}{\sqrt{3-\sqrt{5}}-\sqrt{2}}-\dfrac{2\sqrt{2}}{\sqrt{3+\sqrt{5}}+\sqrt{2}}\)

\(=\dfrac{2\sqrt{2}\cdot\sqrt{2}}{\sqrt{6-2\sqrt{5}}-2}-\dfrac{2\sqrt{2}\cdot2}{\sqrt{6+2\sqrt{5}}+2}\)

\(=\dfrac{4}{\sqrt{5}-1-2}-\dfrac{4}{\sqrt{5}+1+2}\)

\(=\dfrac{4}{\sqrt{5}-3}-\dfrac{4}{\sqrt{5}+3}\)

\(=\dfrac{4\left(\sqrt{5}+3\right)-4\left(\sqrt{5}-3\right)}{5-9}\)

\(=\dfrac{4\sqrt{5}+12-4\sqrt{5}+12}{-4}=\dfrac{-16}{4}=-4\)