If for non-zero, x, x2 - 4x - 1 = 0, the value of x^2 + 1x^2 is?

Answer: Option D

$$\begin{array}{rl}& \iff x^2-4x-1=0\\ & \iff x^2-1=4x\\ & \left(\text{divide }x\text{ both sides}\right)\\ & \iff x-\frac{1}{x}=4\\ & \iff x^2+\frac{1}{x^2}-2=16\\ & \iff x^2+\frac{1}{x^2}=18\end{array}$$