# Wow. Such summation. Much variables. Very degrees.

Algebra Level pending

If the minimum value of $$c$$ that satisfy the inequality for all $$x_{1},x_{2},\dots,x_{n} \geq 0$$

$\displaystyle \large \sum\limits_{1 \leq i < j \leq n} x_{i}x_{j}\left(x_{i}^{2}+x_{j}^{2}\right) \leq c \left(\sum\limits_{1 \leq i \leq n} x_{i}\right)^{4}$

can be expressed as $$\displaystyle \frac{a}{b}$$ for coprime integers $$\large a,b$$. What is the value of $$a^{3}+b^{3}$$?

If $$\displaystyle c <0$$, then $$\displaystyle a < 0$$ and $$\displaystyle b > 0$$.

• This problem is not original.
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