Question 23
Show that if the real numbers $a, b, c$ satisfy the relations
$$
\begin{aligned}
& a+b+c=4 \\
& a^{2}+b^{2}+c^{2}=6
\end{aligned}
$$
then
$$
\frac{86}{9} \leq a^{3}+b^{3}+c^{3} \leq 10.
$$
$$
\begin{aligned}
& a+b+c=4 \\
& a^{2}+b^{2}+c^{2}=6
\end{aligned}
$$
then
$$
\frac{86}{9} \leq a^{3}+b^{3}+c^{3} \leq 10.
$$