If $$x + \frac{1}{x} = 2{\text{,}}$$   then the value of $$\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\left( {{x^3} + \frac{1}{{{x^3}}}} \right)$$     is?

Solution (By Examveda Team)

$$\eqalign{ & x + \frac{1}{x} = 2 \cr & {\text{Put x = 1}} \cr & \therefore {\text{1 + }}\frac{1}{{\left( 1 \right)}} = 2 \cr & \Rightarrow 2 = 2{\text{ }}\left( {{\text{Satisty}}} \right) \cr & \therefore \left( {{x^2} + \frac{1}{{{x^2}}}} \right)\left( {{x^3} + \frac{1}{{{x^3}}}} \right) \cr & = \left( {1 + 1} \right)\left( {1 + 1} \right) \cr & = 2 \times 2 \cr & = 4 \cr} $$