The Sum of Max and Min

★ 7/10Extrema Convexity algebra inequality

Problem

Nonnegative reals $a, b, c$ satisfy $a + b + c = 1$ . Let $M$ and $m$ be the maximum and minimum of

a^3 + 2b^2 + \frac{10}{3}c.

Find $M + m$ .

Answer

Solution

Difficulty	7/10
Topics	Extrema, Convexity, algebra, inequality

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