Question 14
Prove the inequality for non-negative $a, b, c$
$$
a \sqrt{3 a^{2}+6 b^{2}}+b \sqrt{3 b^{2}+6 c^{2}}+c \sqrt{3 c^{2}+6 a^{2}} \geq (a+b+c)^{2}.
$$
$$
a \sqrt{3 a^{2}+6 b^{2}}+b \sqrt{3 b^{2}+6 c^{2}}+c \sqrt{3 c^{2}+6 a^{2}} \geq (a+b+c)^{2}.
$$