If x = 3 + 2 2 , then the value of ( x - 1 x ) is:

Answer: Option B

$$\begin{array}{rl}& {\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)}^2\\ & =x+\frac{1}{x}-2\\ & =\left(3+2\sqrt{2}\right)+\frac{1}{\left(3+2\sqrt{2}\right)}-2\\ & =\left(3+2\sqrt{2}\right)+\frac{1}{\left(3+2\sqrt{2}\right)}\times \frac{\left(3-2\sqrt{2}\right)}{\left(3-2\sqrt{2}\right)}-2\\ & =\left(3+2\sqrt{2}\right)+\left(3-2\sqrt{2}\right)-2\\ & =4\\ & \therefore \left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)=2\end{array}$$