If x = 3 2 + 3 , then the value of x^3 + 1x^3 is?

Answer: Option D

$$\begin{array}{rl}& x=\text{root}3\text{of}2+\sqrt{3}\\ & x^3=2+\sqrt{3}\\ & \frac{1}{x^3}=\frac{1}{2+\sqrt{3}}\times \frac{2-\sqrt{3}}{2-\sqrt{3}}=2-\sqrt{3}\\ & \therefore x^3\text{ + }\frac{1}{x^3}\\ & =2+\sqrt{3}+2-\sqrt{3}\\ & =4\end{array}$$