Đáp án:
$ (x;y) = (2;5) ; (0;-1);(3;5);(-1-1)$
Giải thích các bước giải:
$xy - x² - y - 1=0$
$→(xy - y) - (x² - 1) - 2 = 0$
$→ y(x - 1) - (x - 1)(x + 1) = 2$
$→(x - 1)(y - x - 1) = 2 $
$TH1: \left \{ {{x-1=1} \atop {y-x-1=2}} \right.→$ $\left \{ {{x = 2} \atop {y - 2 - 1 = 2 }} \right.→\left \{ {{x=2} \atop {y = 5}} \right.$
$TH2 : \left \{ {{x -1=-1} \atop {y-x-1=-2}} \right.→\left \{ {{x=0} \atop {y - 0-1=2}} \right.→\left \{ {{x=0} \atop {y=-1}} \right.$
$TH3 : \left \{ {{x-1=2} \atop {y-x-1=1}} \right.→\left \{ {{x=3} \atop {y-3-1=1}} \right.→$ $\left \{ {{x=3} \atop {y=5}} \right.$
$TH4 : \left \{ {{x-1=-2} \atop {y-x-1=-1}} \right.→\left \{ {{x=-1} \atop {y+1-1=-1}} \right.→\left \{ {{x=-1} \atop {y=-1}} \right.$
Vậy$ (x;y) = (2;5) ; (0;-1);(3;5);(-1-1)$
