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At least one nonnegative

Source: Kyiv City MO 2024 Round 2, Problem 7.1

February 4, 2024
algebrainequalities

Problem Statement

Prove that for any real numbers x,y,zx, y, z at least one of numbers x2+y+14,y2+z+14,z2+x+14x^2 + y + \frac{1}{4}, y^2 + z + \frac{1}{4}, z^2 + x + \frac{1}{4} is nonnegative.
Proposed by Oleksii Masalitin
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