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Problem 2 -- One Not More Than One

Source: 46th Austrian Mathematical Olympiad Regional Competition Problem 2

July 14, 2018
Austrianumber theory

Problem Statement

Let xx, yy, and zz be positive real numbers with x+y+z=3x+y+z = 3. Prove that at least one of the three numbers x(x+y−z)x(x+y-z) y(y+z−x)y(y+z-x) z(z+x−y)z(z+x-y) is less or equal 11.
(Karl Czakler)
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