Question

Thu gọn các biểu thức sau:

\(\dfrac{2}{2+\sqrt{5}}+2\sqrt{5}\)

Answer 1

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

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

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

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

Answer 2

Ta có: \(\dfrac{2}{\sqrt{5}+2}+2\sqrt{5}\)

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

\(=4\sqrt{5}-4\)