Đáp án:(x;y)=(1;-10); (-1;14); (2;-4); (-2;8); (3;-2); (-3;6); (12;1); (-12;3); (6;0); (-6;4); (4;-1); (-4;5)
Giải thích các bước giải:
x(y-2)=-12
⇒x; y-2∈Z
⇒x; y-2∈UC(-12)={-1;1;-2;2;-3;3;-4;4;-6;6;-12;12}
⇒(1)$\left \{ {{x=1} \atop {y-2=-12}} \right.$⇔ $\left \{ {{x=1} \atop {y=-10}} \right.$
⇒(2)$\left \{ {{x=-1} \atop {y-2=12}} \right.$⇔ $\left \{ {{x=-1} \atop {y=14}} \right.$
⇒(3)$\left \{ {{x=2} \atop {y-2=-6}} \right.$⇔ $\left \{ {{x=2} \atop {y=-4}} \right.$
⇒(4)$\left \{ {{x=-2} \atop {y-2=6}} \right.$⇔ $\left \{ {{x=-2} \atop {y=8}} \right.$
⇒(5)$\left \{ {{x=3} \atop {y-2=-4}} \right.$⇔ $\left \{ {{x=3} \atop {y=-2}} \right.$
⇒(6)$\left \{ {{x=-3} \atop {y-2=4}} \right.$⇔ $\left \{ {{x=-3} \atop {y=6}} \right.$
⇒(7)$\left \{ {{x=12} \atop {y-2=-1}} \right.$⇔ $\left \{ {{x=12} \atop {y=1}} \right.$
⇒(8)$\left \{ {{x=-12} \atop {y-2=1}} \right.$⇔ $\left \{ {{x=-12} \atop {y=3}} \right.$
⇒(9)$\left \{ {{x=6} \atop {y-2=-2}} \right.$⇔ $\left \{ {{x=6} \atop {y=0}} \right.$
⇒(10)$\left \{ {{x=-6} \atop {y-2=2}} \right.$⇔ $\left \{ {{x=-6} \atop {y=4}} \right.$
⇒(11)$\left \{ {{x=4} \atop {y-2=-3}} \right.$⇔ $\left \{ {{x=4} \atop {y=-1}} \right.$
⇒(12)$\left \{ {{x=-4} \atop {y-2=3}} \right.$⇔ $\left \{ {{x=-4} \atop {y=5}} \right.$
⇒(x;y)=(1;-10); (-1;14); (2;-4); (-2;8); (3;-2); (-3;6); (12;1); (-12;3); (6;0); (-6;4); (4;-1); (-4;5)
