Problem A. 642. (April 2015)

A. 642. Let \(\displaystyle n\ge3\), let \(\displaystyle x_1,\ldots,x_n\) be nonnegative numbers, and let \(\displaystyle A=\sum_{i=1}^n x_i\), \(\displaystyle B= \sum_{i=1}^n x_i^2\) and \(\displaystyle C= \sum_{i=1}^n x_i^3\). Prove that \(\displaystyle (n+1)A^2B + (n-2)B^2 \ge A^4 + (2n-2)AC\).

(5 pont)

Deadline expired on May 11, 2015.

Statistics:

10 students sent a solution.
5 points:	Csépai András, Di Giovanni Márk, Fehér Zsombor, Janzer Barnabás, Schrettner Bálint, Szabó 789 Barnabás, Williams Kada.
4 points:	Adnan Ali, Glasznova Maja.
3 points:	1 student.

Problems in Mathematics of KöMaL, April 2015