Question

If a+b+c=0, find the value of $\frac{a^4+b^4+c^4}{a^2{b}^2+c^2(a^2+b^2)}$

Answer 1

$a+b+c=0$ means $a+b=-c$
or $a^2+b^2+2ab=c^2$
or $a^2+b^2-c^2=2ab$
squaring $a^4+b^4-c^4=2(a^2{b}^2+b^2{c}^2+c^2{a}^2)$
or $\frac{a^4+b^4+c^4}{a^2{b}^2+c^2(a^2+b^2)}=2$