SOLUTION: Stuck on solving this type of question. x^8 + x^16 = 1. Also if you have time 2*x^16(x^(8)-1) = x^24 - 1 These are arising in financial mathematics problem I am working

Question 726261: Stuck on solving this type of question.
x^8 + x^16 = 1.
Also if you have time
2*x^16(x^(8)-1) = x^24 - 1
These are arising in financial mathematics problem I am working on.
I do know the answers as they are given, but no idea how to simplify or solve this problem by hand.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
------------------------------------------------------
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
===============================
Cheers,
Stan H.

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