If ( x + 1/x ) = 13 , then the value of ( x^3 - 1x^3 ) is = ?

Answer: Option D

$$\begin{array}{rl}& \left(x+\frac{1}{x}\right)=\sqrt{13}\\ & \Rightarrow {\left(x+\frac{1}{x}\right)}^2-4={\left(\sqrt{13}\right)}^2-4\\ & \Rightarrow {\left(x-\frac{1}{x}\right)}^2=9\\ & \Rightarrow \left(x-\frac{1}{x}\right)=3\\ & \Rightarrow {\left(x-\frac{1}{x}\right)}^3=3^3=27\\ & \Rightarrow x^3-\frac{1}{x^3}-3.x.\frac{1}{x}\left(x-\frac{1}{x}\right)=27\\ & \Rightarrow x^3-\frac{1}{x^3}-3\times 3=27\\ & \Rightarrow x^3-\frac{1}{x^3}=27+9=36\end{array}$$