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