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Let x, y, and z be nonzero real numbers, such that no two are equal, and x + 1/y = y + 1/z = z + 1/x. Find all possible numeric values of xyz.

 

Thanks!

 

Please explain how you got your answer. CPhill, if you are available, please answer this!!

 Feb 1, 2021
edited by Destryox  Feb 1, 2021
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Try letting x = a and y = 1/b.  Then you should get the result that xyz can be -2, -1, 1 or 2.

 Feb 3, 2021

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