Tìm x y thuộc n sao cho x y – 5 x + y = 17

Đáp án:

\[\left( {x;y} \right) = \left\{ {\left( {0;17} \right);\left( {11;6} \right);\left( {1;11} \right);\left( {5;7} \right);\left( {2;9} \right);\left( {3;8} \right)} \right\}\]

Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
xy – 5x + y = 17\\
 \Leftrightarrow \left( {xy – 5x} \right) + \left( {y – 5} \right) = 17 – 5\\
 \Leftrightarrow x\left( {y – 5} \right) + \left( {y – 5} \right) = 12\\
 \Leftrightarrow \left( {x + 1} \right)\left( {y – 5} \right) = 12\\
x,y \in N \Rightarrow x + 1 \ge 1\\
12 = 1.12 = 2.6 = 3.4\\
 \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x + 1 = 1\\
y – 5 = 12
\end{array} \right.\\
\left\{ \begin{array}{l}
x + 1 = 12\\
y – 5 = 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x + 1 = 2\\
y – 5 = 6
\end{array} \right.\\
\left\{ \begin{array}{l}
x + 1 = 6\\
y – 5 = 2
\end{array} \right.\\
\left\{ \begin{array}{l}
x + 1 = 3\\
y – 5 = 4
\end{array} \right.\\
\left\{ \begin{array}{l}
x + 1 = 4\\
y – 5 = 3
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x = 0\\
y = 17
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 11\\
y = 6
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 1\\
y = 11
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 5\\
y = 7
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 2\\
y = 9
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 3\\
y = 8
\end{array} \right.
\end{array} \right.\\
 \Rightarrow \left( {x;y} \right) = \left\{ {\left( {0;17} \right);\left( {11;6} \right);\left( {1;11} \right);\left( {5;7} \right);\left( {2;9} \right);\left( {3;8} \right)} \right\}
\end{array}\)