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JBMO 2016 No 2 - Ketaksamaan tak homogen, dengan pecahan-pecahan bertebaran

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Misal $a,b,c$ merupakan bilangan real positif. Buktikan bahwa $$\frac{8}{(a+b)^2+4abc}+\frac{8}{(b+c)^2+4abc}+\frac{8}{(c+a)^2+4abc}+a^2+b^2+c^2\geq \frac{8}{a+3}+\frac{8}{b+3}+\frac{8}{c+3}$$

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