Question 72
Find all values of the real parameter $a$ such that the solutions of the system
$$
\begin{cases} \frac{3x-5}{3} + \frac{3x+5}{4} \ge \frac{x}{7} - \frac{1}{15} \\ (2x-a)^3 + (2x+a)(1-4x^2) + 16x^2a - 6xa^2 + a^3 \le 2a^2 + a \end{cases}
$$
form an interval of length $\frac{32}{225}$.
$$
\begin{cases} \frac{3x-5}{3} + \frac{3x+5}{4} \ge \frac{x}{7} - \frac{1}{15} \\ (2x-a)^3 + (2x+a)(1-4x^2) + 16x^2a - 6xa^2 + a^3 \le 2a^2 + a \end{cases}
$$
form an interval of length $\frac{32}{225}$.