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.
By symmetry, x = y = z. So the possible values of xyz are 8 and -8.
how do you know that x = y = z?
It says that no two are equal, so how can \(x=y=z\)?
+133 
