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[DOTOANNANG]

Cho $a, b, c> 0$. Chứng minh:

$\frac{\sqrt{a^{3}+ b^{3}}}{a^{2}+ b^{2}}+ \frac{\sqrt{b^{3}+ c^{3}}}{b^{2}+ c^{2}} +\frac{\sqrt{c^{3}+ a^{3}}}{c^{2}+ a^{2}}\geq \frac{6\left ( ab+ bc +ca \right )}{\left ( a+ b+ c \right )\sqrt{\left ( a+ b \right )\left ( a+ c \right )\left ( c+ a \right )}}$