If x⁴ - 6x² - 1 = 0, then the value of $${x^6} - 5{x^2} + \frac{5}{{{x^2}}} - \frac{1}{{{x^6}}} + 5$$     is:

Solution (By Examveda Team)

$$\eqalign{ & {x^4} - 6{x^2} - 1 = 0, \cr & {x^2}\left( {{x^2} - 6 - \frac{1}{{{x^2}}}} \right) = 0 \cr & {x^2} - \frac{1}{{{x^2}}} = 6 \cr & {x^6} - \frac{1}{{{x^6}}} = 216 + 18 = 234 \cr & {x^6} - \frac{1}{{{x^6}}} - 5\left( {{x^2} - \frac{1}{{{x^2}}}} \right) + 5 \cr & = 234 - 30 + 5 \cr & = 209 \cr} $$