If x - 1/x = 2 , then the value of the following is x^3 - 1x^3 = ?

Answer: Option D

$$\begin{array}{rl}& x-\frac{1}{x}=2\text{ to find }{x}^3-\frac{1}{x^3}\\ & \Rightarrow x-\frac{1}{x}=2\\ & \left[\text{Cubing both sides}\right]\\ & \Rightarrow {\left(x-\frac{1}{x}\right)}^3={\left(2\right)}^3\\ & \Rightarrow x^3-\frac{1}{x^3}-3\times x\times \frac{1}{x}\left(x-\frac{1}{x}\right)=8\\ & \Rightarrow x^3-\frac{1}{x^3}-3\times \left(2\right)=8\\ & \Rightarrow x^3-\frac{1}{x^3}=14\end{array}$$