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Let x, y, and z be nonzero real numbers, such that no two are equal, and \(x + \frac{1}{y} = y + \frac{1}{z} = z + \frac{1}{x}.\)Find all possible numeric values of xyz.

 Aug 28, 2020
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The set of all possible values of xyz is 1, -1, 2, and -2

 Aug 28, 2020

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