If $${x^4} + \frac{1}{{{x^4}}} = 14159,$$    then the value of $$x + \frac{1}{x}$$  is:

Solution (By Examveda Team)

$$\eqalign{ & {x^4} + \frac{1}{{{x^4}}} = 14159 \cr & {x^2} + \frac{1}{{{x^2}}} = \sqrt {14159 + 2} \cr & {x^2} + \frac{1}{{{x^2}}} = 119 \cr & x + \frac{1}{x} = \sqrt {119 + 2} \cr & x + \frac{1}{x} = 11 \cr} $$