A Quintic Product Bound

Problem

For positive reals $a, b, c$ , prove that

\left(a^5 - a^2 + 3\right)\left(b^5 - b^2 + 3\right)\left(c^5 - c^2 + 3\right) \ge (a+b+c)^3.

Answer

Solution

Difficulty	9/10
Topics	AM-GM, inequality

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