Question 2
Let $a,b,c$ be nonnegative real numbers. Prove
$$3(a^2+b^2+c^2)\ge(a+b+c)(\sqrt{ab}+\sqrt{bc}+\sqrt{ca})+(a-b)^2+(b-c)^2+(c-a)^2\ge(a+b+c)^2.$$
$$3(a^2+b^2+c^2)\ge(a+b+c)(\sqrt{ab}+\sqrt{bc}+\sqrt{ca})+(a-b)^2+(b-c)^2+(c-a)^2\ge(a+b+c)^2.$$