\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-1\right)\left(y-2\right)=12\\\left(x-1\right)^2+\left(y-2\right)^2=25\end{matrix}\right.\) \(\Rightarrow\) đặt \(\left\{{}\begin{matrix}x-1=a\\y-2=b\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}ab=12\\a^2+b^2=25\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}b=\dfrac{12}{a}\\a^2+\dfrac{144}{a^2}=25\end{matrix}\right.\) \(\Leftrightarrow a^4-25a^2+144=0\Rightarrow\left[{}\begin{matrix}a^2=16\\a^2=9\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}a=4\Rightarrow b=3\\a=-4\Rightarrow b=-3\\a=3\Rightarrow b=4\\a=-3\Rightarrow b=-4\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=5;y=5\\x=-3;y=-1\\x=4;y=6\\x=-2;y=-2\end{matrix}\right.\)
Hệ đã cho có 4 cặp nghiệm \(\left(x;y\right)=\left(5;5\right);\left(-3;-1\right);\left(4;6\right);\left(-2;-2\right)\)
