If x⁴ + x^-4 = 194, x > 0, then the value of (x - 2)² is:

Solution (By Examveda Team)

$$\eqalign{ & {x^4} + \frac{1}{{{x^4}}} = 194, \cr & {x^4} + \frac{1}{{{x^4}}} + 2 = 194 + 2 \cr & {x^2} + \frac{1}{{{x^2}}} + 2 = 16 \cr & x + \frac{1}{x} = 4 \cr & {x^2} + 1 = 4x \cr & {x^2} - 4x = - 1 \cr & {x^2} - 4x + 1 = 0 \cr & {x^2} - 4x + 4 - 3 = 0 \cr & {x^2} - 4x + 4 = 3 \cr & {\left( {x - 2} \right)^2} = 3 \cr} $$