Question

Tính giá trị biểu thức:

\(\dfrac{5+\sqrt{5}}{\sqrt{5}+2}\) + \(\dfrac{5}{\sqrt{5}-1}\) - \(\dfrac{3\sqrt{5}}{3+\sqrt{5}}\)

Answer 1

\(E=\left(5+\sqrt{5}\right)\left(\sqrt{5}-2\right)+\dfrac{5\left(\sqrt{5}+1\right)}{4}-\dfrac{3\sqrt{5}\left(3-\sqrt{5}\right)}{4}\)

\(=5\sqrt{5}-10+5-2\sqrt{5}+\dfrac{5\sqrt{5}+5-9\sqrt{5}+15}{4}\)

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