Solve the system of equations for positive real numbers:

Question

1/xy = x/z + 1, 1/yz = y/x + 1, 1/zx = z/y + 1.

Answer 1

By symmetry, we conclude at least one solution is x=y=z.
Assume p=x=y=z, then
1/p^2=p/p+1=2
Can you solve for p?

Answer 2

how does 2 came
1/p^2=p/p+1=2

Answer 3

p/p=1