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abc >= 4038^3 if 1/(a + 2019)+1/(b + 2019)+1/(c + 2019)=1/2019

Source: New Zealand NZMOC Camp Selection Problems 2018 p5

September 19, 2021
algebrainequalities

Problem Statement

Let a,ba, b and cc be positive real numbers satisfying 1a+2019+1b+2019+1c+2019=12019.\frac{1}{a + 2019}+\frac{1}{b + 2019}+\frac{1}{c + 2019}=\frac{1}{2019}. Prove that abc≥40383abc \ge 4038^3.
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