Question

Tìm x, y biết:

x² - 3x - xy + 3y = 7

Answer 1

\(x^2-3x-xy+3y=7\)

\(\Rightarrow x\left(x-3\right)-y\left(x-3\right)=7\)

\(\Rightarrow\left(x-y\right)\left(x-3\right)=7\)

\(\Rightarrow x-y;x-3\inƯ\left(7\right)\)

\(Ư\left(7\right)=\left\{\pm1;\pm7\right\}\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-3=1\Rightarrow x=4\\x-y=7\Rightarrow y=-3\end{matrix}\right.\\\left\{{}\begin{matrix}x-3=-1\Rightarrow x=2\\x-y=-7\Rightarrow y=9\end{matrix}\right.\\\left\{{}\begin{matrix}x-3=7\Rightarrow=10\\x-y=1\Rightarrow y=9\end{matrix}\right.\\\left\{{}\begin{matrix}x-3=-7\Rightarrow x=-4\\x-y=-1\Rightarrow y=-3\end{matrix}\right.\end{matrix}\right.\)