Question

Rút gọn 

\(\dfrac{1}{\sqrt{11-2\sqrt{30}}}-\dfrac{3}{7-2\sqrt{10}}\)

Answer 1

\(=\dfrac{1}{\sqrt{11-2\sqrt{5}.\sqrt{6}}}-\dfrac{3\left(7+2\sqrt{10}\right)}{\left(7-2\sqrt{10}\right)\left(7+2\sqrt{10}\right)}\\ =\dfrac{1}{\sqrt{\left(\sqrt{5}-\sqrt{6}\right)^2}}-\dfrac{3\left(7+2\sqrt{10}\right)}{49-40}\\ =\dfrac{1}{\left|\sqrt{5}-\sqrt{6}\right|}-\dfrac{7+2\sqrt{10}}{3}\\ =\dfrac{1}{\sqrt{6}-\sqrt{5}}-\dfrac{7+2\sqrt{10}}{3}\\ =\dfrac{\sqrt{6}+\sqrt{5}}{6-5}-\dfrac{7+2\sqrt{10}}{3}\\ =\sqrt{6}+\sqrt{5}+\dfrac{7+2\sqrt{10}}{3}\\ =\dfrac{3\sqrt{6}+3\sqrt{5}+7+2\sqrt{10}}{3}\)

Answer 2

\(=\dfrac{1}{\sqrt{6}-\sqrt{5}}+\dfrac{7+2\sqrt{10}}{3}\)

\(=\sqrt{6}+\sqrt{5}+\dfrac{7}{3}+\dfrac{2}{3}\sqrt{10}\)