1 câu trả lời
Đáp án: $(x,y)\in\{(3,4), (4, 0), (5,-2), (1,-6), (0, -2), (-1,0)\}$
Giải thích các bước giải:
Ta có:
$xy-2y-4=3x-x^2$
$\to xy-2y=4+3x-x^2$
$\to y(x-2)=4+3x-x^2$
Vì $x,y\in Z\to y(x-2)\quad\vdots\quad x-2$
$\to 4+3x-x^2\quad\vdots\quad x-2$
$\to 3x-(x^2-4)\quad\vdots\quad x-2$
$\to 3x-(x-2)(x+2)\quad\vdots\quad x-2$
$\to 3x\quad\vdots\quad x-2$
$\to 3(x-2)+6\quad\vdots\quad x-2$
$\to 6\quad\vdots\quad x-2$
$\to x-2\in U(6)$
$\to x-2\in\{1,2,3,-1,-2,-3\}$
$\to x\in\{3,4,5,1,0,-1\}$
$\to y\in\{4, 0, -2, -6, -2, 0\}$ vì $y(x-2)=4+3x-x^2\to y=\dfrac{4+3x-x^2}{x-2}$
$\to (x,y)\in\{(3,4), (4, 0), (5,-2), (1,-6), (0, -2), (-1,0)\}$
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