\(a\left(a+b+c\right)=-12\)
\(b\left(a+b+c\right)=18\)
\(c\left(a+b+c\right)=30\)
\(a\left(a+b+c\right)+b\left(a+b+c\right)+c\left(a+b+c\right)=-12+18+30\)
\(\left(a+b+c\right)\left(a+b+c\right)=36\)
\(\left(a+b+c\right)^2=\left(\pm6\right)^2\)
\(a+b+c=\pm6\)
Th1:
\(a+b+c=6\)
\(\left[\begin{array}{nghiempt}a\times6=-12\\b\times6=18\\c\times6=30\end{array}\right.\)
\(\left[\begin{array}{nghiempt}a=-\frac{12}{6}\\b=\frac{18}{6}\\c=\frac{30}{6}\end{array}\right.\)
\(\left[\begin{array}{nghiempt}a=-2\\b=3\\c=5\end{array}\right.\)
Th2:
\(a+b+c=-6\)
\(\left[\begin{array}{nghiempt}a\times\left(-6\right)=-12\\b\times\left(-6\right)=18\\c\times\left(-6\right)=30\end{array}\right.\)
\(\left[\begin{array}{nghiempt}a=\frac{-12}{-6}\\b=\frac{18}{-6}\\c=\frac{30}{-6}\end{array}\right.\)
\(\left[\begin{array}{nghiempt}a=2\\b=-3\\c=-5\end{array}\right.\)
