Để pt có 2 nghiệm pb:
\(\left\{{}\begin{matrix}a\ne0\\\Delta=9\left(a+1\right)^2-4a\left(2a+4\right)>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a\ne0\\\left(a+1\right)^2+8>0\end{matrix}\right.\) \(\Rightarrow a\ne0\)
Theo Viet ta có: \(\left\{{}\begin{matrix}x_1+x_2=\frac{-3\left(a+1\right)}{a}\\x_1x_2=\frac{2a+4}{a}\end{matrix}\right.\)
\(x_1^2+x_2^2=4\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2=4\)
\(\Leftrightarrow\left(\frac{-3\left(a+1\right)}{a}\right)^2-\frac{2\left(2a+4\right)}{a}=4\)
\(\Leftrightarrow9a^2+18a+9-4a^2-8a=4a^2\)
\(\Leftrightarrow a^2+10a+9=0\Rightarrow\left[{}\begin{matrix}a=-1\\a=-9\end{matrix}\right.\)
