Let $a$,$b$,$c$ be real positive numbers. Prove that \[\left(\frac{a^3+abc}{b+c}\right)+\left(\frac{b^3+abc}{c+a}\right)+\left(\frac{c^3+abc}{a+b}\right)\ge a^2+b^2+c^2\]
Let $a,b$ and $c$ be sides of a triangle. Prove that: $\frac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}+\frac{\sqrt{c+a-b}}{\sqrt{c}+\sqrt{a}-\sqrt{b}}+\frac{\sqrt{a+b-c}}{\sqrt{a}+\sqrt{b}-\sqrt{c}}\leq 3$