Question

tìm nghiệm nguyên của phương trình 2x²y+x+y+1=2x²+xy+y²

Answer 1

\(\Leftrightarrow2x^2\left(y-1\right)-x\left(y-1\right)-y\left(y-1\right)=-1\)\(\Leftrightarrow\left(y-1\right)\left(2x^2-x-y\right)=-1\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}y-1=-1\\2x^2-x-y=1\end{matrix}\right.\\\left\{{}\begin{matrix}y-1=1\\2x^2-x-y=-1\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}\left[{}\begin{matrix}x=1\left(TM\right)\\x=\dfrac{-1}{2}\left(KTM\right)\end{matrix}\right.\\y=0\end{matrix}\right.\\\left\{{}\begin{matrix}\left[{}\begin{matrix}x=1\left(TM\right)\\x=\dfrac{-1}{2}\left(KTM\right)\end{matrix}\right.\\y=2\end{matrix}\right.\end{matrix}\right.\)

Vậy pt có nghiệm là (1;0);(1;2).