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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.

 May 26, 2021
 #1
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You can isolate x, y, z to get that the possible values of xyz are -2, -1, 1, and 2.

 May 27, 2021

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