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.
Please explain how you got your answer. CPhill, if you are available, please answer this!!
Try letting x = a and y = 1/b. Then you should get the result that xyz can be -2, -1, 1 or 2.