Tìm các cặp số nguyên (x;y) sao cho (2x + 1)(y – 3) = -6
Câu hỏi:
Tìm các cặp số nguyên (x;y) sao cho (2x + 1)(y – 3) = -6
Ta có: (2x + 1)(y – 3) = -6
=> (2x + 1)(y – 3) = -1.6 = 1.(-6)=2.(-3)=(-2).3
* (2x + 1)(y – 3) = -1.6
\( \Rightarrow \left\{ \begin{array}{l}
2x + 1 = – 1\\
y – 3 = 6
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = – 1\\
y = 9
\end{array} \right.\)
Hoặc \( \Rightarrow \left\{ \begin{array}{l}
2x + 1 = 6\\
y – 3 = – 1
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = \frac{5}{2}\\
y = 2
\end{array} \right.\)
* (2x + 1)(y – 3) = 1. (-6)
\( \Rightarrow \left\{ \begin{array}{l}
2x + 1 = 1\\
y – 3 = – 6
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 0\\
y = – 3
\end{array} \right.\)
Hoặc \( \Rightarrow \left\{ \begin{array}{l}
2x + 1 = – 6\\
y – 3 = – 1
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = – \frac{7}{2}\\
y = 4
\end{array} \right.\)
* (2x + 1)(y – 3) = 2. (-3)
\( \Rightarrow \left\{ \begin{array}{l}
2x + 1 = 2\\
y – 3 = – 3
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = \frac{1}{2}\\
y = 0
\end{array} \right.\)
Hoặc \( \Rightarrow \left\{ \begin{array}{l}
2x + 1 = 6\\
y – 3 = – 1
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = \frac{5}{2}\\
y = 2
\end{array} \right.\)
* (2x + 1)(y – 3) = (-2).3
\( \Rightarrow \left\{ \begin{array}{l}
2x + 1 = – 2\\
y – 3 = 3
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = \frac{{ – 3}}{2}\\
y = 6
\end{array} \right.\)
Hoặc \( \Rightarrow \left\{ \begin{array}{l}
2x + 1 = 3\\
y – 3 = – 2
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 1\\
y = 1
\end{array} \right.\)
Vậy tìm được 4 cặp số nguyên (x; y) là (-1; 9); (0; -3); (-2; 5); (1; 1)
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Tag: Tìm các cặp số nguyên (x;y) sao cho (2x + 1)(y – 3) = -6