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1/2 <= (a^3+b^3)/(a^2+b^2) <= 1 for positive with a+b = 1

Source: Mathematics Regional Olympiad of Mexico West 2021 P1

September 9, 2022
algebrainequalities

Problem Statement

Let aa and bb be positive real numbers such that a+b=1a+b = 1. Prove that 12≤a3+b3a2+b2≤1\frac12 \le \frac{a^3+b^3}{a^2+b^2} \le 1
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