Question

\(\dfrac{1}{5+2\sqrt{6}}-\dfrac{1}{5-2\sqrt{6}}\)

Rút gọn !!!

 

Answer 1

\(\dfrac{1}{5+2\sqrt{6}}-\dfrac{1}{5-2\sqrt{6}}=\dfrac{5-2\sqrt{6}-5-2\sqrt{6}}{5^2-\left(2\sqrt{6}\right)^2}=\dfrac{-4\sqrt{6}}{25-24}=-4\sqrt{6}\)

Answer 2

\(=\dfrac{5-2\sqrt{6}-5-2\sqrt{6}}{\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}=\dfrac{-4\sqrt{6}}{25-24}=-4\sqrt{6}\)

Answer 3

Ta có: \(\dfrac{1}{5+2\sqrt{6}}-\dfrac{1}{5-2\sqrt{6}}\)

\(=5-2\sqrt{6}-5-2\sqrt{6}\)

\(=-4\sqrt{6}\)