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x^{1994} +1/x^{1994} if x +1/x=-1 (Chile NMO 1994 P5)

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November 21, 2021
algebra

Problem Statement

Let xx be a number such that x+1x=−1x +\frac{1}{x}=-1. Determine the value of x1994+1x1994x^{1994} +\frac{1}{x^{1994}}.
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