If x = 5 + 2 6 , then x - 1 x = is?

Answer: Option A

$$\begin{array}{rl}& {\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)}^2\\ & =x+\frac{1}{x}-2\\ & =\left(5+2\sqrt{6}\right)+\frac{1}{\left(5+2\sqrt{6}\right)}-2\\ & =\left(5+2\sqrt{6}\right)+\frac{1}{\left(5+2\sqrt{6}\right)}\times \frac{\left(5-2\sqrt{6}\right)}{\left(5-2\sqrt{6}\right)}-2\\ & =\left(5+2\sqrt{6}\right)+\left(5-2\sqrt{6}\right)-2\\ & =10-2\\ & =8\\ & \therefore \left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)=\sqrt{8}=2\sqrt{2}\end{array}$$