Question 125
Given two moving points $A(x_1, y_1)$ and $B(x_2, y_2)$ on parabola curve $y^2 = 6x$ with $x_1 + x_2 = 4$ and $x_1 \neq x_2$, and the perpendicular bisector of segment $AB$ intersects $x$-axis at point $C$. Find the maximum area of $\triangle ABC$.