If ( x + 1/x ) = 2, then ( x - 1/x ) is equal to = ?

Answer: Option A

$$\begin{array}{rl}& \left(x+\frac{1}{x}\right)\text{ = 2}\\ & \Rightarrow {\left(x+\frac{1}{x}\right)}^2\text{ = }{\text{2}}^2\\ & \Rightarrow x^2+\frac{1}{x^2}+2=4\\ & \Rightarrow x^2+\frac{1}{x^2}=2\\ & \Rightarrow x^2+\frac{1}{x^2}-2.x.\frac{1}{x}\\ & =2-2=0\\ & \Rightarrow {\left(x-\frac{1}{x}\right)}^2\text{ = 0}\\ & \Rightarrow x-\frac{1}{x}=0\end{array}$$