If x^2 + 1x^2 = 66 , then the value of x^2 - 1 + 2xx = ?

Answer: Option B

$$\begin{array}{rl}& x^2+\frac{1}{x^2}=66\\ & \text{Subtract 2 from both sides}\\ & \Rightarrow x^2+\frac{1}{x^2}-2=66-2\\ & \Rightarrow {\left(x+\frac{1}{x}\right)}^2=64\\ & \Rightarrow {\left(x+\frac{1}{x}\right)}^2={\left(8\right)}^2\\ & \Rightarrow x-\frac{1}{x}=\pm 8\\ & \Rightarrow \frac{x^2-1+2x}{x}\\ & \Rightarrow \frac{\frac{x^2}{x}-\frac{1}{x}+\frac{2x}{x}}{\frac{x}{x}}\\ & \Rightarrow \frac{\left(x-\frac{1}{x}\right)+2}{1}\\ & \text{When , }x-\frac{1}{x}=+8\\ & \text{Then,}\\ & \left(x-\frac{1}{x}\right)+2=8+2=10\\ & \text{When }x-\frac{1}{x}=-8\\ & \Rightarrow x-\frac{1}{x}=-8+2\\ & \Rightarrow x-\frac{1}{x}=-6\\ & \therefore \left(10,-6\right)\end{array}$$