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)
$$\eqalign{ & c + \frac{1}{c} = \sqrt 3 \cr & {\text{On cubing both side}} \cr & \Rightarrow {\left( {c + \frac{1}{c}} \right)^3} = 3\sqrt 3 \cr & \Rightarrow {c^3} + \frac{1}{{{c^3}}} + 3.c.\frac{1}{c}\left( {c + \frac{1}{c}} \right) = 3\sqrt 3 \cr & \Rightarrow {c^3} + \frac{1}{{{c^3}}} + 3\sqrt 3 = 3\sqrt 3 \cr & \Rightarrow {c^3} + \frac{1}{{{c^3}}} = 3\sqrt 3 - 3\sqrt 3 \cr & \Rightarrow {c^3} + \frac{1}{{{c^3}}} = 0 \cr} $$This Question Belongs to Arithmetic Ability >> Algebra
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