Question

If x+1/x=1 ,then find x^7+1/x^7 ?

Answer 1

Answer:

Assume that x7 + 1/x7 = 0. Then: x7 = -1/x7 x7x7 = -1 x14 = -1. Therefore x is an imaginary number. Now by hypothesis we know that x + x-1 = 1. Since x is imaginary, x-1 is also imaginary. By the closure property of the set of imaginary numbers, x + x-1 must also be imaginary. However, the hypothesis states that x + x-1 = 1, which is not imaginary. Thus by contradiction, if x + 1/x = 1, then x7 + 1/x7 = 1.

Source https://www.physicsforums.com/threads/prove-if-x-1-x-1-then-x-7-1-x-7-1.861265/