If $${x^2} + \frac{1}{{{x^2}}} = 38,$$   then what is the value of $$\left( {x - \frac{1}{x}} \right)?$$

A. 9

B. 5

C. 6

D. 4

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & {x^2} + \frac{1}{{{x^2}}} = 38 \cr & {x^2} + \frac{1}{{{x^2}}} - 2 = 38 - 2 \cr & {\left( {x - \frac{1}{x}} \right)^2} = 36 \cr & x - \frac{1}{x} = 6 \cr} $$