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Given $x + 1/ x = - 2$ , evaluate $x^{2025} + 1/ x^{2025}$ .

Competition practiceAlgebra

A−2
B2
C0
D1

Step-by-Step Solution

x + 1/ x = - 2

gives

(x + 1)^{2} = 0

, so

x = - 1

. An odd power of −1 is −1, so the sum is

- 1 + (- 1) = - 2

.

Answer: A) −2

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