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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 values of \(xyz.\)

 

--------Thanks! cool

 Apr 15, 2020
 #1
avatar+20957 
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This will be true if x = y = z.

 Apr 16, 2020
 #2
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It says in the question that no two are equal

AnExtremelyLongName  Apr 16, 2020

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