Question 12
Find, with proof, the largest possible value of
$$
\frac{x_{1}^{2}+\cdots+x_{n}^{2}}{n}
$$
where real numbers $x_{1}, \ldots, x_{n} \geq -1$ are satisfying $x_{1}^{3}+\cdots+x_{n}^{3}=0$.
$$
\frac{x_{1}^{2}+\cdots+x_{n}^{2}}{n}
$$
where real numbers $x_{1}, \ldots, x_{n} \geq -1$ are satisfying $x_{1}^{3}+\cdots+x_{n}^{3}=0$.