Question 15
A1 (POL), IMO2. Let $n\ge2$ be a fixed integer. Find the least constant $C$ such that the inequality
$$\sum_{i\lt j}x_ix_j(x_i^2+x_j^2)\le C\left(\sum_i x_i\right)^4$$
holds for every $x_1,\ldots,x_n\ge0$ (the sum on the left consists of $\binom n2$ summands). For this constant $C$, characterize the instances of equality.
$$\sum_{i\lt j}x_ix_j(x_i^2+x_j^2)\le C\left(\sum_i x_i\right)^4$$
holds for every $x_1,\ldots,x_n\ge0$ (the sum on the left consists of $\binom n2$ summands). For this constant $C$, characterize the instances of equality.