Toán Lớp 8: tìm x,y là số nguyên thỏa: x^2-x+xy-y=0
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Toán Lớp 8: tìm x,y là số nguyên thỏa: x^2-x+xy-y=0
Comments ( 2 )
{x^2} – x + xy – y = 0\\
\Rightarrow \left( {{x^2} – x} \right) + \left( {xy – y} \right) = 0\\
\Rightarrow x\left( {x – 1} \right) + y\left( {x – 1} \right) = 0\\
\Rightarrow \left( {x + y} \right)\left( {x – 1} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
x – 1 = 0\\
x + y = 0
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x = 1\\
thay\,\,x = 1
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x = 1\\
y = – 1
\end{array} \right.\\
\Rightarrow S \in \{ – 1;1\}
\end{array}\]