If x - 1/x = 3 , then the value of x^3 - 1x^3\, is?

Answer: Option B

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