Question 138
Find all values of the real parameter $a$ for which the solution set of the system of inequalities
$$
\begin{cases} |x-2| + |x-1| + |x+3| \le 6 \\ x^2 - a x + 2a \le 0 \end{cases}
$$
is a closed interval of length 1.
$$
\begin{cases} |x-2| + |x-1| + |x+3| \le 6 \\ x^2 - a x + 2a \le 0 \end{cases}
$$
is a closed interval of length 1.