If x + 1/x = 1 then what would be the value of x^(1729) + x^(-1729)

Question

If
x + 1/x = 1
then
x^(1729) + x^(-1729) = ?

Answer 1

(X+1/X)^2 = X^2 + 1/X^2 + 2
(X+1/X)^1729 = X^1729 + 1/X^1729 + 2 { 1/X=X^-1 ...... 1/X^1729=X^-1729....}
(X+1/X)^1729 = X^1729 + X^-1729 + 2
X^1729 + X^-1729 = (X+1/X)^1729 - 2
X^1729 + X^-1729 = 1^1729 - 2 {X + 1/X = 1...........}
X^1729 + X^-1729 = 1-2
X^1729 + X^-1729 = -1