Thread: How to simplify this system of equations?

Can You help me to simplify this system of equations?:

x-y+z=6
x**2+y**2+z**2=14
x**3-y**3+z**3=36

Somewhere, I made a mistake in my calculations. I wound up with one minus sign too many. But I know what the result is. See the attached file.

6= xyz