Question 6
Let $a,b$ and $c$ be three non-zero real numbers that satisfy $a+b+c=0$. What is the value of
$$S=\frac{a^4}{a^4-(b^2-c^2)^2}+\frac{b^4}{b^4-(c^2-a^2)^2}+\frac{c^4}{c^4-(a^2-b^2)^2}?$$
$$S=\frac{a^4}{a^4-(b^2-c^2)^2}+\frac{b^4}{b^4-(c^2-a^2)^2}+\frac{c^4}{c^4-(a^2-b^2)^2}?$$