MathDB
Simple inequality

Source: 2018 PRMO (IMO selection Stage -1 in india)

September 29, 2018
inequalitiesalgebra

Problem Statement

What is the largest positive integer nn such that a2b29+c31+b2c29+a31+c2a29+b31≥n(a+b+c)\frac{a^2}{\frac{b}{29} + \frac{c}{31}}+\frac{b^2}{\frac{c}{29} + \frac{a}{31}}+\frac{c^2}{\frac{a}{29} + \frac{b}{31}} \ge n(a+b+c)holds for all positive real numbers a,b,ca,b,c.
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