If $$\frac{{{x^8} + 1}}{{{x^4}}} = 14,$$   then the value of $$\frac{{{x^{12}} + 1}}{{{x^6}}}$$  is:

Solution (By Examveda Team)

$$\eqalign{ & \frac{{{x^8} + 1}}{{{x^4}}} = 14 \cr & {x^4} + \frac{1}{{{x^4}}} = 14 \cr & {x^2} + \frac{1}{{{x^2}}} = 4 \cr & {x^6} + \frac{1}{{{x^6}}} = {4^3} - 3 \times 4 \cr & {x^6} + \frac{1}{{{x^6}}} = 64 - 12 \cr & \frac{{{x^{12}} + 1}}{{{x^6}}} = 52 \cr} $$