Question

\(\left\{{}\begin{matrix}x^2+x+y^2+y=18\\xy\left(x+1\right)\left(y+1\right)=72\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}x^2+x+y^2+y=18\\xy\left(x+1\right)\left(y+1\right)=72\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\left(x+1\right)+y\left(y+1\right)=18\\x\left(x+1\right).y\left(y+1\right)=72\end{matrix}\right.\)

Đặt \(a=x\left(x+1\right);b=y\left(y+1\right)\) thì

\(\left\{{}\begin{matrix}a+b=18\\ab=72\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}a=12\\b=6\end{matrix}\right.\\\left\{{}\begin{matrix}a=6\\b=12\end{matrix}\right.\end{matrix}\right.\)

Đến đây dễ rồi nha ^^