Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.2 National olympiad Prove it

Theorem 3.6 If $a, b, c \in R_{+}$ , then we have: $\sum \frac{a^{3}}{b+c}-\frac{a^{2}+b^{2}+c^{2}}{2} \geq \frac{1}{6} \sum(2 a-b-c)^{2}$

Solution

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