Mathematical and Physical Journal
for High Schools
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Problem A. 371. (April 2005)

A. 371. Given that a+b\lec+1, b+c \lea+1, c+a\leb+1 for the numbers a,b,c \ge0, show that a2+b2+c2\le2abc+1.

(5 pont)

Deadline expired on May 17, 2005.


Statistics:

9 students sent a solution.
5 points:Jankó Zsuzsanna, Király Csaba, Kiss-Tóth Christian, Mánfay Máté, Paulin Roland, Seres Gyula, Strenner Balázs.
1 point:2 students.

Problems in Mathematics of KöMaL, April 2005