Question

A= \(\dfrac{10\sqrt{6}-12}{\sqrt{6}-5}\)-\(3\sqrt{\dfrac{2}{3}}\)+\(\dfrac{15}{\sqrt{6}-1}\)

Tính

Answer 1

Ta có: \(A=\dfrac{10\sqrt{6}-12}{\sqrt{6}-5}-3\sqrt{\dfrac{2}{3}}+\dfrac{15}{\sqrt{6}-1}\)

\(=\dfrac{-2\sqrt{6}\left(5-\sqrt{6}\right)}{5-\sqrt{6}}-\sqrt{\dfrac{2}{3}\cdot9}+\dfrac{15\left(\sqrt{6}+1\right)}{\left(\sqrt{6}-1\right)\left(\sqrt{6}+1\right)}\)

\(=-2\sqrt{6}-\sqrt{6}+3\left(\sqrt{6}+1\right)\)

\(=-3\sqrt{6}+3\sqrt{6}+3\)

=3