Find all the real system solutions:
$$2x+x^2y=y$$
$$2y+y^2z=z$$
$$2z+z^2x=x$$
My attempt
Trivial solution : (0,0,0)
We have:
$$frac{1}{y}=frac{1-x^2}{2x}$$
$$frac{1}{z}=frac{1-y^2}{2y}$$
$$frac{1}{x}=frac{1-z^2}{2z}$$
Then:
$$x+frac{1}{x} + y+frac{1}{y} + z+frac{1}{z}=0$$
How to procede?
