If $$2x + \frac{1}{{2x}} = 2,$$   then what is the value of $$\sqrt {2{{\left( {\frac{1}{x}} \right)}^4} + {{\left( {\frac{1}{x}} \right)}^5}} ?$$

Solution (By Examveda Team)

$$\eqalign{ & 2x + \frac{1}{{2x}} = 2 \cr & {\text{Now, }}2x = 1 \cr & \Rightarrow x = \frac{1}{2} \cr & \Rightarrow \frac{1}{x} = 2 \cr & \sqrt {2{{\left( {\frac{1}{x}} \right)}^4} + {{\left( {\frac{1}{x}} \right)}^5}} \cr & = \sqrt {2 \times {2^4} + {2^5}} \cr & = \sqrt {32 + 32} \cr & = \sqrt {64} \cr & = 8 \cr} $$