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# pls help hard question about polynomials

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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

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By symmetry, x = y = z.  So the possible values of xyz are 8 and -8.

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

SpicyP  Jun 14, 2020
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It says that no two are equal, so how can $$x=y=z$$?

Guest Jun 17, 2020