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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

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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!

Jan 26, 2021

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You can isolate x, y, z to get that the possible values of xyz are -2, -1, 1, and 2.

Jan 26, 2021
#2
+70
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Sorry, will you please explain how you got that? i want to be able to solve these problems again in the future.

Jan 27, 2021
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For the community: Please don't submit solutions to this problem. This is a homework problem for an online course that does not allow students to search for answers to specific problems outside of the school.

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The answer given by guest is incorrect, as are all of the other responses to this question currently on this site.

Feb 2, 2021