Let $a, b, c$ be positive reals. Prove that $$\sqrt{abc}(\sqrt{a} +\sqrt{b} +\sqrt{c}) + (a + b + c)^2 \ge 4 \sqrt{3abc(a + b + c)}.$$
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Tags: inequalities, 3rd edition
Let $a, b, c$ be positive reals. Prove that $$\sqrt{abc}(\sqrt{a} +\sqrt{b} +\sqrt{c}) + (a + b + c)^2 \ge 4 \sqrt{3abc(a + b + c)}.$$