Question 65
Over all pairs of complex numbers $(x, y)$ satisfying the equations
$$
x + 2y^{2} = x^{4} \quad \text{and} \quad y + 2x^{2} = y^{4}
$$
compute the minimum possible real part of $x$.
$$
x + 2y^{2} = x^{4} \quad \text{and} \quad y + 2x^{2} = y^{4}
$$
compute the minimum possible real part of $x$.