\(\left\{{}\begin{matrix}\left(x+y\right)^2-xy=19\\\left(x+y\right)-xy=-1\end{matrix}\right.\) \(\Rightarrow\left(x+y\right)^2-\left(x+y\right)-20=0\)
\(\Rightarrow\left[{}\begin{matrix}x+y=5\Rightarrow xy=6\\x+y=-4\Rightarrow xy=-3\end{matrix}\right.\)
- Với \(\left\{{}\begin{matrix}x+y=5\\xy=6\end{matrix}\right.\) theo Viet đảo x;y là nghiệm:
\(t^2-5t+6=0\Rightarrow\left[{}\begin{matrix}t=2\\t=3\end{matrix}\right.\)
\(\Rightarrow\left(x;y\right)=\left(2;3\right);\left(3;2\right)\)
- Với \(\left\{{}\begin{matrix}x+y=-4\\xy=-3\end{matrix}\right.\) theo Viet đảo x;y là nghiệm:
\(t^2+4t-3=0\Rightarrow\left[{}\begin{matrix}t=-2-\sqrt{7}\\t=-2+\sqrt{7}\end{matrix}\right.\)
\(\Rightarrow\left(x;y\right)=\left(-2-\sqrt{7};-2+\sqrt{7}\right);\left(-2+\sqrt{7};-2-\sqrt{7}\right)\)
