Đáp án: $(x,y)\in\{(2,1),(3,2), (1,1), (1,2),(2,3)\}$
Giải thích các bước giải:
Ta có:
$\begin{cases}x+1\quad\vdots\quad y\\ y+1\quad\vdots\quad x\end{cases}$
Vì $x,y\in N^*\to x+1,y+1>0$
$\to \begin{cases}x+1\ge y\\ y+1\ge x\end{cases}$
$\to \begin{cases}x+1\ge y\\ y\ge x-1\end{cases}$
$\to x+1\ge y\ge x-1$
$\to y\in\{x+1, x,x-1\}$
Trường hợp $1: y=x+1$
$\to (x+1)+1\quad\vdots\quad x$
$\to x+2\quad\vdots\quad x$
$\to 2\quad\vdots\quad x$
$\to x\in\{2,1\}$
$\to y\in\{3,2\}$
$\to (x,y)\in\{(2,3), (1,2)$
Trường hợp $2: y=x$
$\to x+1\quad\vdots\quad x$
$\to 1\quad\vdots\quad x$
$\to x\in\{1\}$
$\to y\in\{1\}$
$\to (x,y)\in\{(1,1)$
Trường hợp $1: y=x-1$
$\to (x+1)\quad\vdots\quad y$
$\to (x+1)\quad\vdots\quad x-1$
$\to (x-1)+2\quad\vdots\quad x-1$
$\to 2\quad\vdots\quad x-1$
$\to x-1\in\{1,2\}$
$\to x\in\{2,3\}$
$\to y\in\{1,2\}$
$\to (x,y)\in\{(2,1),(3,2)\}$
