hi. I'm not sure if this is a right topic but i have got problem with solving 2 inequalities:

(1) Numbers a,b,c are lengths of sides of a triangle, which square equals S, and let p,q,r be positive reals such that p+q+r=1. Prove that $\displaystyle \frac{p}{q+r}\cdot a^{2}+\frac{q}{p+r}\cdot b^{2}+\frac{r}{q+p}\cdot c^{2} \geqslant 2\sqrt{3}\cdot S$.

(2) Let a,b,c be positive reals, and n positive integer. Prove that $\displaystyle \frac{a^{n+1}}{b+c}+\frac{b^{n+1}}{a+c}+\frac{c^{n +1}}{b+a}\geqslant (\frac{a^{n}}{b+c}+\frac{a^{n}}{b+c}+\frac{a^{n}}{ b+c})\cdot (\frac{a^{n}+b^{n}+c^{n}}{3})^{\frac{1}{n}}$.

It is possible that it came from previous olympics (if its true its unlikely to be IMO, because I have already checked some of recent exercises. Then If you remember any of it just let me know source