I have this system of two equations I'm trying to solve:
$$-(1+\alpha) x^3 + (\alpha y +1) x^2 - (1+\alpha) \beta^2 x + \alpha\beta ^2 y = 0$$ $$-(1+\alpha) y^3 + (\alpha x +\epsilon) y^2 - (1+\alpha) \beta^2 y + \alpha\beta ^2 x = 0$$
It is easy to see that (0,0) is one solution of this problem, but I'm having trouble in finding the others.
Any ideas?