Question 15
Let $a,b,c$ be positive real numbers. Prove
$$\frac a{b+c}+\frac b{c+a}+\frac c{a+b}+\sqrt{\frac{ab+bc+ca}{a^2+b^2+c^2}}\ge\frac52.$$
When does equality hold?
$$\frac a{b+c}+\frac b{c+a}+\frac c{a+b}+\sqrt{\frac{ab+bc+ca}{a^2+b^2+c^2}}\ge\frac52.$$
When does equality hold?