Question 106
Over all real numbers $x$ and $y$ such that
$$
x^{3}=3 x+y \quad \text{ and } \quad y^{3}=3 y+x
$$
compute the sum of all possible values of $x^{2}+y^{2}$.
$$
x^{3}=3 x+y \quad \text{ and } \quad y^{3}=3 y+x
$$
compute the sum of all possible values of $x^{2}+y^{2}$.