IMO Shortlist 1991 problem 26
Dodao/la:
arhiva2. travnja 2012. Determine the maximum value of the sum
over all
![n -](/media/m/3/3/9/339dbad977d3cb6a3910b2a8efab3502.png)
tuples
![(x_1, \ldots, x_n),](/media/m/9/8/0/980bb551e5201b606101b5a582b7cc61.png)
satisfying
![x_i \geq 0](/media/m/f/7/4/f74817decd7078f57c8ade92942ef4c4.png)
and
%V0
Determine the maximum value of the sum
$$\sum_{i < j} x_ix_j (x_i + x_j)$$
over all $n -$tuples $(x_1, \ldots, x_n),$ satisfying $x_i \geq 0$ and $\sum^n_{i = 1} x_i = 1.$
Izvor: Međunarodna matematička olimpijada, shortlist 1991