Question 427260
We can square both sides to obtain


{{{x^2 + (1/x^2) - 2 = 4}}} --> {{{x^2 + (1/x^2) = 6}}}. Square both sides again to get


{{{x^4 + (1/x^4) + 2 = 36}}} --> {{{x^4 + (1/x^4) = 34}}}. Repeat.


{{{x^8 + (1/x^8) + 2 = 1156}}}, so {{{x^8 + (1/x^8) = 1154}}}.