If $$x + \frac{{16}}{x} = 8,$$   then the value of $${x^2} + \frac{{32}}{{{x^2}}}$$  is:

Solution (By Examveda Team)

$$\eqalign{ & x + \frac{{16}}{x} = 8 \cr & {\text{at }}x = 4{\text{ it satisfy}} \cr & {x^2} + \frac{{32}}{{{x^2}}} = {4^2} + \frac{{32}}{{{4^2}}} \cr & = 16 + 2 \cr & = 18 \cr} $$