Question

Tìm ác cặp số nguyên x,y thỏa mãn

5x² +2xy+y² -4x -40=0

Answer 1

\(\Leftrightarrow\left(x+y\right)^2+\left(2x-2\right)^2=36=0^2+6^2\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+y=0\\2x-2=6\end{matrix}\right.\\\left\{{}\begin{matrix}x+y=6\\2x-2=0\end{matrix}\right.\\\left\{{}\begin{matrix}x+y=-6\\2x-2=0\end{matrix}\right.\\\left\{{}\begin{matrix}x+y=0\\2x-2=-6\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=4\\y=-4\end{matrix}\right.\\\left\{{}\begin{matrix}x=1\\y=5\end{matrix}\right.\\\left\{{}\begin{matrix}x=1\\y=-7\end{matrix}\right.\\\left\{{}\begin{matrix}x=-2\\y=2\end{matrix}\right.\end{matrix}\right.\)(TM)

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