If $${x^2} + \frac{1}{{{x^2}}} = 7,$$   then the value of $${x^3} + \frac{1}{{{x^3}}}$$  where x > 0 is equal to:

A. 18

B. 12

C. 15

D. 16

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & {x^2} + \frac{1}{{{x^2}}} = 7 \cr & x + \frac{1}{x} = 3 \cr & {x^3} + \frac{1}{{{x^3}}} = {3^3} - 3 \times 3 = 18 \cr} $$