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