Problem

Source: Peru Ibero TST 2018

Tags: algebra



Let $p, q$ be real numbers. Knowing that there are positive real numbers $a, b, c$, different two by two, such that $$p=\frac{a^2}{(b-c)^2}+\frac{b^2}{(a-c)^2}+\frac{c^2}{(a-b)^2},$$$$q=\frac{1}{(b-c)^2}+\frac{1}{(a-c)^2}+\frac{1}{(b-a)^2}$$calculate the value of $$\frac{a}{(b-c)^2}+\frac{b}{(a-c)^2}+\frac{c}{(b-a)^2}$$in terms of $p, q$.