# Math Help - Find all real numbers x, y and z?

1. ## Find all real numbers x, y and z?

Find all real numbers x, y, z such that 1/xy = (x/z) + 1, 1/yz = (y/x) + 1, 1/zx = (z/y) + 1

2. Originally Posted by fardeen_gen
Find all real numbers x, y, z such that 1/xy = (x/z) + 1, 1/yz = (y/x) + 1, 1/zx = (z/y) + 1
you are just solving 3 equations in 3 unknowns.. you can do it..

3. From the symmetry of the equations, try x = y = z, which gives $(x,y,z)=\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2} },\frac{1}{\sqrt{2}}\right)$.