<s>[INST] Prove that $a+b+c\le 0$ $a,b,c$ are integer numbers different from zero and 
$$\frac{a}{b+c^2}=\frac{a+c^2}{b}$$
Prove that $a+b+c\le 0$.
I know how to prove that $a+b<0$ but do not know what about $c$.
 [/INST] Since $c \in \mathbb{Z}$, we have $c \le |c|\le c^2$
$$0=(a+b)c^2+c^4$$
$$a+b+c^2=0$$
$$a+b+c \le a+b+c^2=0$$
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