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

A. 4

B. 10

C. 12

D. 18

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & \Leftrightarrow {x^2} - 4x - 1 = 0 \cr & \Leftrightarrow {x^2} - 1 = 4x \cr & \left( {{\text{divide }}x{\text{ both sides}}} \right) \cr & \Leftrightarrow x - \frac{1}{x} = 4 \cr & \Leftrightarrow {x^2} + \frac{1}{{{x^2}}} - 2 = 16 \cr & \Leftrightarrow {x^2} + \frac{1}{{{x^2}}} = 18 \cr} $$