If x = 5 + 2√6, then what is the value of x + 1 x ?

Answer: Option A

$$\begin{array}{rl}& x=5+2\sqrt{6}\\ & \Rightarrow x={\left(\sqrt{3}+\sqrt{2}\right)}^2\\ & \Rightarrow \sqrt{x}=\sqrt{3}+\sqrt{2}\\ & \Rightarrow \frac{1}{\sqrt{x}}=\sqrt{3}-\sqrt{2}\\ & \Rightarrow \sqrt{x}+\frac{1}{\sqrt{x}}=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}\\ & \Rightarrow \sqrt{x}+\frac{1}{\sqrt{x}}=2\sqrt{3}\end{array}$$