Problem of the Day #105

POTD March 23, 2024

Let x_1 and x_2 be the roots of the equation y = \left|3-2\sqrt{-4x^2+24x-27}\right|. Let m be the value of the global maximum of this graph (no calculus needed). If the value of m\cdot\left|x_1-x_2\right| can be expressed as \frac{a\sqrt{b}}{c}, where a, b, and c are positive integers, \gcd{(a, c)} = 1, and c is not divisible by the square of any prime, find a+b+c.