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# Algebra 2 Question

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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!

Apr 15, 2020

#1
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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