If x = 5 + 2√6, then what is the value of $$\sqrt x + \frac{1}{{\sqrt x }}?$$

Solution (By Examveda Team)

$$\eqalign{ & x = 5 + 2\sqrt 6 \cr & \Rightarrow x = {\left( {\sqrt 3 + \sqrt 2 } \right)^2} \cr & \Rightarrow \sqrt x = \sqrt 3 + \sqrt 2 \cr & \Rightarrow \frac{1}{{\sqrt x }} = \sqrt 3 - \sqrt 2 \cr & \Rightarrow \sqrt x + \frac{1}{{\sqrt x }} = \sqrt 3 + \sqrt 2 + \sqrt 3 - \sqrt 2 \cr & \Rightarrow \sqrt x + \frac{1}{{\sqrt x }} = 2\sqrt 3 \cr} $$