\(\hept{\begin{cases}x^2-4x+3=0\\x^2+xy+y^2=1\end{cases}\Leftrightarrow}\hept{\begin{cases}\left(x-1\right)\left(x-3\right)=0\\x^2+xy+y^2=1\end{cases}}\)
\(\Leftrightarrow\left(I\right)\hept{\begin{cases}x=1\\x^2+xy+y^2=1\end{cases}\left(h\right)\left(II\right)\hept{\begin{cases}x=3\\x^2+xy+y^2=1\end{cases}}}\)
Giải hệ (I) \(\hept{\begin{cases}x=1\\x^2+xy+y^2=1\end{cases}\Leftrightarrow}\hept{\begin{cases}x=1\\1+y+y^2=1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=1\\y^2+y=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x=1\\y\left(y+1\right)=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x=1\\y=0\end{cases}\left(h\right)\hept{\begin{cases}x=1\\y=-1\end{cases}}}\)
Giải hệ (II)\(\hept{\begin{cases}x=3\\x^2+xy+y^2=1\end{cases}\Leftrightarrow}\hept{\begin{cases}x=3\\9+3y+y^2=1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=3\\y^2+3y+8=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=3\\\left(y+\frac{3}{2}\right)^2+\frac{23}{4}=0\end{cases}}\)hệ vô nghiệm
