If $$c + \frac{1}{c} = \sqrt 3 {\text{,}}$$   then the value of $${c^3} + \frac{1}{{{c^3}}}$$   is equal to?

A. 0

B. $$\frac{3}{{\sqrt 3 }}$$

C. $$\frac{1}{{\sqrt 3 }}$$

D. $$\frac{6}{{\sqrt 3 }}$$

Answer: Option A

Solution(By Examveda Team)

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