While doing inequality problems from a exercise I stuck on the following two problems.
$1.$ If $a,b,c$ be positive real numbers, such that the sum of any two is greater than the third, prove that $a^2 (p-q)(p-r)+b^2 (q-p)(q-r)+c^2 (r-p)(r-q)>0$ for all real $p,q,r.$
$2.$ If $a,b,c$ be positive real numbers, not all equal, and $n$ is a negative rational number, prove that $a^n (a-b)(a-c)+b^n (b-a)(b-c)+c^n (c-a)(c-b) >0$ No need of a full solution. Just give me some hint. I want to do this myself