If $$x + \frac{1}{x} \ne 0$$   and $${x^3} + \frac{1}{{{x^3}}} = 0{\text{,}}$$   then the value $${\left( {x + \frac{1}{x}} \right)^4}$$   is?

Solution (By Examveda Team)

$$\eqalign{ & {x^3} + \frac{1}{{{x^3}}} = 0{\text{ }} \cr & {\text{It is possible only when}} \cr & x + \frac{1}{x} = \sqrt 3 {\text{ }} \cr & {\text{So, }}{\left( {x + \frac{1}{x}} \right)^4} = {\left( {\sqrt 3 } \right)^4} \cr & \Leftrightarrow {\left( {x + \frac{1}{x}} \right)^4} = 9 \cr} $$