If $$x + \left( {\frac{1}{x}} \right) = 2{\text{,}}$$   then the value of $${x^7}{\text{ + }}\left( {\frac{1}{{{x^5}}}} \right)$$   is?

Solution (By Examveda Team)

$$\eqalign{ & x + \frac{1}{x} = 2 \cr & {\text{Find , }}{x^7} + \frac{1}{{{x^5}}} \cr & \,\,\,\,\,\,\,x + \frac{1}{x} = 2 \cr & \Rightarrow \mathop \downarrow \limits_1 {\text{ }}\,\,\,\,{\text{ }}\mathop \downarrow \limits_1 \,\,\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow {\text{Let }}x = 1 \cr & {\text{To put value in question,}} \cr & \Rightarrow {x^7} + \frac{1}{{{x^5}}} \cr & \Rightarrow {{\text{1}}^7} + \frac{1}{{{1^5}}} \cr & \Rightarrow 1 + 1 \cr & \Rightarrow 2 \cr} $$