Mathematical and Physical Journal
for High Schools
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Problem A. 422. (March 2007)

A. 422. Let x1,x2,...,xn,xn+1 be positive real numbers with x1+x2+...+xn=xn+1. Prove that

\sum_{i=1}^n\sqrt{x_i(x_{n+1}-x_i)} \le \sqrt{\sum_{i=1}^n x_{n+1}(x_{n+1}-x_i)}.

Romanian competition problem

(5 pont)

Deadline expired on April 16, 2007.

Statistics:

21 students sent a solution.
5 points:Bogár 560 Péter, Dobribán Edgár, Honner Balázs, Kisfaludi-Bak Sándor, Kónya 495 Gábor, Korándi Dániel, Kutas Péter, Lovász László Miklós, Sümegi Károly, Varga 171 László.
4 points:Gyenizse Gergő, Hujter Bálint, Kornis Kristóf, Nagy 235 János, Nagy 314 Dániel, Szilágyi Dániel, Tomon István.
3 points:2 students.
2 points:1 student.
Unfair, not evaluated:1 solutions.

Problems in Mathematics of KöMaL, March 2007