Question 184·Hard·Nonlinear Equations in One Variable; Systems in Two Variables

In the $xy$-plane, the graph of $y = x^3 - 6x$ intersects the graph of $y = x$ at three points. One of the intersection points is $(0,0)$, and the other two are $(a,a)$ and $(-a,-a)$. What is the value of $a^2$?