Very strange inequality..
Posted: Sun Jun 18, 2017 10:43 pm
Let $a$,$b$,$c$ be real positive numbers. Prove that
\[\left(\frac{a^3+abc}{b+c}\right)+\left(\frac{b^3+abc}{c+a}\right)+\left(\frac{c^3+abc}{a+b}\right)\ge a^2+b^2+c^2\]
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\[\left(\frac{a^3+abc}{b+c}\right)+\left(\frac{b^3+abc}{c+a}\right)+\left(\frac{c^3+abc}{a+b}\right)\ge a^2+b^2+c^2\]
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