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# Let x, y, and z be nonzero real numbers, such that no two are equal, and Find all possible numeric values of xyz.

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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 8, 2022