Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.2 National olympiad Prove it

Inference 3.8 If $a, b, c \in R_{+}$ , then: $\sum \frac{a^{2}}{b+c}-\frac{a+b+c}{2} \geq \frac{2\left(a^{3}+b^{3}+c^{3}-3 a b c\right)}{(a+b+c)^{2}}$

Solution

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