If c + 1/c = 3 , then the value of c^3 + 1c^3 is equal to?

Answer: Option A

$$\begin{array}{rl}& c+\frac{1}{c}=\sqrt{3}\\ & \text{On cubing both side}\\ & \Rightarrow {\left(c+\frac{1}{c}\right)}^3=3\sqrt{3}\\ & \Rightarrow c^3+\frac{1}{c^3}+3.c.\frac{1}{c}\left(c+\frac{1}{c}\right)=3\sqrt{3}\\ & \Rightarrow c^3+\frac{1}{c^3}+3\sqrt{3}=3\sqrt{3}\\ & \Rightarrow c^3+\frac{1}{c^3}=3\sqrt{3}-3\sqrt{3}\\ & \Rightarrow c^3+\frac{1}{c^3}=0\end{array}$$