G3.2 Let $a, b$ and $c$ be real numbers. If 1 is a root of $x^{2}+a x+2=0$ and $a$ and $b$ be roots of $x^{2}+5 x+c=0$, find the value of $a+b+c$.
$\begin{array}{l}1+a+2=0 \Rightarrow a=-3 \\ -3+b=-5 \Rightarrow b=-2 \\ c=-3 b=6 \\ a+b+c=1\end{array}$