1. Cho $a,b,c$ dương, chứng minh:
$$ \frac{a^3+b^3+c^3}{3abc}+ \frac{a(b+c)}{b^2+c^2}+\frac{b(a+c)}{a^2+c^2}+\frac{c(a+b)}{a^2+b^2} \geq 4$$
2. Cho $a,b,c$ dương, chứng minh:
$$ \frac{a^2}{b+c}+\frac{b^2}{a+c}+\frac{c^2}{b+a} \geq \frac{3}{2}\frac{a^3+b^3+c^3}{a^2+b^2+c^2}$$