Đáp án:
a, \((x,y) \in \left\{ {(0,8),(2,2)(8,0)} \right\}\)
b, \((x,y) \in \left\{ {(3,1),(1,5),(0,13)} \right\}\)
c, \((x,y) \in \left\{ {(7,0),(2,1),(1,2),(0,7)} \right\}\)
Giải thích các bước giải:
\(\begin{array}{l}
a,xy + x + y = 8\\
\Leftrightarrow xy + x + y + 1 = 9\\
\Leftrightarrow (x + 1)(y + 1) = 9\\
\Rightarrow x + 1 \in \left\{ {1,3,9} \right\}\\
\Rightarrow (x,y) \in \left\{ {(0,8),(2,2)(8,0)} \right\}\\
b,(x + 1)(y + 2) + x = 15\\
\Leftrightarrow (x + 1)(y + 2) + x + 1 = 16\\
\Leftrightarrow (x + 1)(y + 3) = 16\\
\Rightarrow y + 3 \in \left\{ {4,8,16} \right\}(y + 3 \ge 3)\\
\Rightarrow (x,y) \in \left\{ {(3,1),(1,5),(0,13)} \right\}\\
c,2xy + x + y = 7\\
\Leftrightarrow 4xy + 2x + 2y = 14\\
\Leftrightarrow 2x(2y + 1) + 2y + 1 = 15\\
\Leftrightarrow (2y + 1)(2x + 1) = 15\\
\Rightarrow 2y + 1 \in \left\{ {1,3,5,15} \right\}\\
\Rightarrow (x,y) \in \left\{ {(7,0),(2,1),(1,2),(0,7)} \right\}
\end{array}\)
