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If $x + 1/ x = 1$ , find the value of $x^{99} + 1/ x^{99}$ .

Competition practiceAlgebra

A2
B−2
C0
D1

Step-by-Step Solution

x^{2} - x + 1 = 0

; multiplying by

x + 1 : x^{3} + 1 = 0

, so

x^{3} = - 1

and

x^{99} = - 1

. Value

= - 1 + (- 1) = - 2

.

Answer: B) −2

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