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Indonesia Regional Inequality

Source: 2024 Indonesia Regional MO Essay Problem 1

May 6, 2024
InequalityinequalitiesalgebraIndonesiaRMO

Problem Statement

Given a real number C⩽2C\leqslant 2. Prove that for every positive real number x,yx,y with xy=1xy=1, the following inequality holds: x2+y22+Cx+y⩾1+C2 \sqrt{\frac{x^2+y^2}{2}} + \frac{C}{x+y} \geqslant 1 + \frac{C}{2}
Proposed by Fajar Yuliawan, Indonesia
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