If x = 3^1/3 - 3^ - 1/3 value of 3x^3 + 9x is?

Answer: Option A

$$\begin{array}{rl}& x=3^{\frac{1}{3}}-3^{-\frac{1}{3}}\\ & \Rightarrow x+3^{-\frac{1}{3}}=3^{\frac{1}{3}}\left(\text{cubing both sides}\right)\\ & \Rightarrow x^3+\frac{1}{3}+3\times x\times 3^{-\frac{1}{3}}\left(x+3^{-\frac{1}{3}}\right)=3\\ & \Rightarrow x^3+\frac{1}{3}+3\times x\times 3^{-\frac{1}{3}}\times 3^{\frac{1}{3}}=3\\ & \left(\text{multiply both sides by 3}\right)\\ & \Rightarrow 3x^3+9x=9-1\\ & \Rightarrow 3x^3+9x=8\end{array}$$