Question 726261
Stuck on solving this type of question. 
x^8 + x^16 = 1.
Convert to a Quadratic Equation Form:
(x^8)^2 + x^8 - 1 = 0
Use the quadratic formula:
x^8 = [-1 +-sqrt(1-4*-1)}/2
x^8 = [-1 +-sqrt(5)]/2
x = the +-8th root of the value on the right side.
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Also if you have time 
2*x^16(x^(8)-1) = x^24 - 1 
2*x^24-2*x^16 = x^24-1
x^24 - 2x^16 + 1 = 0
Solution: x = 1 or x = -1
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Cheers,
Stan H.