It is known that the number of real solutions of the following system if finite. Prove that this system has an even number of solutions: $(y^2+6)(x-1)=y(x^2+1)$ $(x^2+6)(y-1)=x(y^2+1)$
Source: Cono Sur 1991-problem 3
Tags: algebra unsolved, algebra
It is known that the number of real solutions of the following system if finite. Prove that this system has an even number of solutions: $(y^2+6)(x-1)=y(x^2+1)$ $(x^2+6)(y-1)=x(y^2+1)$