MathDB
Inequality (idk what to say)

Source: Russian TST 2016, Day 10 P3 (Group A), P4 (Group B)

April 19, 2023
algebrainequalities

Problem Statement

Let a,b,ca,b,c be positive real numbers such that a2+b2+c2⩾3a^2+b^2+c^2\geqslant 3. Prove that a2a+b2+b2b+c2+c2c+a2⩾32.\frac{a^2}{a+b^2}+\frac{b^2}{b+c^2}+\frac{c^2}{c+a^2}\geqslant\frac{3}{2}.
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