Question 32
Find all the real $\left(a, b, c\right)$ triplets checking the equalities system: $$
\left\{
\begin{array}{l}
a\left(b^{2}+c\right)=c(c+a b) \\
b\left(c^{2}+a\right)=a(a+b c) \\
c\left(a^{2}+b\right)=b(b+a c)
\end{array}
\right.
$$
\left\{
\begin{array}{l}
a\left(b^{2}+c\right)=c(c+a b) \\
b\left(c^{2}+a\right)=a(a+b c) \\
c\left(a^{2}+b\right)=b(b+a c)
\end{array}
\right.
$$