If x = 1 ( 2 + 1 ) , the value of x2 + 2x - 1 is?

Answer: Option C

$$\begin{array}{rl}& \text{Given that,}\\ & x=\frac{1}{\left(\sqrt{2}+1\right)}\\ & \text{Then, }{x}^2+2x-1\\ & =x^2+2x-1+1-1\\ & =x^2+2x+1-2\\ & ={\left(x+1\right)}^2-2\\ & \text{Now put the value of }x\\ & ={\left(\frac{1}{\left(\sqrt{2}+1\right)}+1\right)}^2-2\\ & ={\left(\frac{1+\sqrt{2}+1}{\sqrt{2}+1}\right)}^2-2\\ & ={\left(\frac{\sqrt{2}+2}{\sqrt{2}+1}\right)}^2-2\\ & ={\left(\frac{\left(\sqrt{2}+1\right)\times \sqrt{2}}{\sqrt{2}+1}\right)}^2-2\\ & ={\left(\sqrt{2}\right)}^2-2\\ & =2-2\\ & =0\end{array}$$