9. Let $n (n \geqslant 2)$ be a fixed integer,
(1) Determine the smallest constant $c$ such that the inequality $\sum_{1 \leqslant i<j \leqslant n} x_{i} x_{j}\left(x_{i}^{2}+x_{j}^{2}\right) \leqslant c\left(\sum_{i=1}^{n} x_{i}\right)^{4}$ holds for all non-negative real numbers $x_{1}, x_{2}, \cdots, x_{n}$;
(2) For this constant $c$, determine the necessary and sufficient conditions for equality to hold.
(IMO - 40 Problem)