Question 78
There are real numbers $a$, $b$ and $c$ such that $f(x) = x^3 + a x^2 + b x + c$ has three real roots $x_1$, $x_2$ and $x_3$ satisfying
$$
(1)\quad x_2 - x_1 = \lambda,
$$
$$
(2)\quad x_3 \gt \frac{1}{2}(x_1 + x_2).
$$
Find the maximum value of $\frac{2a^3 + 27c - 9ab}{\lambda^3}$.
$$
(1)\quad x_2 - x_1 = \lambda,
$$
$$
(2)\quad x_3 \gt \frac{1}{2}(x_1 + x_2).
$$
Find the maximum value of $\frac{2a^3 + 27c - 9ab}{\lambda^3}$.