Đáp án: $(x,y)\in\{(2, 2), (3,3)\}$

 

Giải thích các bước giải:

Ta có:

$xy-1\quad\vdots\quad (x-1)(y-1)$

$\to \begin{cases}xy-1\quad\vdots\quad x-1\\xy-1\quad\vdots\quad y-1\end{cases}$

$\to \begin{cases}y(x-1)+y-1\quad\vdots\quad x-1\\x(y-1)+x-1\quad\vdots\quad y-1\end{cases}$

$\to \begin{cases}y-1\quad\vdots\quad x-1\\x-1\quad\vdots\quad y-1\end{cases}$

$\to \begin{cases}y-1\ge x-1\\ x-1\ge y-1\end{cases}$ vì $x,y>1$

$\to \begin{cases}y\ge x\\x\ge y\end{cases}$

$\to x=y$

$\to x^2-1\quad\vdots\quad (x-1)^2$

$\to (x-1)(x+1)\quad\vdots\quad (x-1)^2$

$\to x+1\quad\vdots\quad x-1$

$\to x-1+2\quad\vdots\quad x-1$

$\to 2\quad\vdots\quad x-1$

$\to x-1\in\{1, 2, -1, -2\}$

$\to x\in\{2, 3, 0, -1\}$

Mà $x>1$

$\to x\in\{2, 3\}$

$\to (x,y)\in\{(2, 2), (3,3)\}$