If $$x - \frac{1}{x} = 3{\text{,}}$$   then the value of $${x^3} - \frac{1}{{{x^3}}}\,{\text{is?}}$$

A. 32

B. 36

C. 40

D. 49

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & x - \frac{1}{x} = 3 \cr & \left( {{\text{By cubing both sides}}} \right) \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} - 3.x.\frac{1}{x}\left( {x - \frac{1}{x}} \right) = 27 \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} - 3.\left( 3 \right) = 27 \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} = 27 + 9 \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} = 36 \cr} $$