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

Answer: Option B

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