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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. 

 Jun 11, 2020
 #1
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By symmetry, x = y = z.  So the possible values of xyz are 8 and -8.

 Jun 12, 2020
 #2
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how do you know that x = y = z?

SpicyP  Jun 14, 2020
 #3
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It says that no two are equal, so how can \(x=y=z\)?

Guest Jun 17, 2020

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