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(a + b)^3/ 4 >= a^2b + ab^2 for a,b>0

Source: New Zealand NZMOC Camp Selection Problems 2014 p1

September 19, 2021
algebrainequalities

Problem Statement

Prove that for all positive real numbers aa and b b: (a+b)34a2b+ab2\frac{(a + b)^3}{4} \ge a^2b + ab^2