Đáp án:a)(x;y)=(2;4); (0;-6); (6;0); (-4;-2)
b)Không có số nguyên x,y
c)(x;y)=(-1;4); (-3;-2); (1;2); (-5;0)
Giải thích các bước giải:
a)(x-1)(y+1)=5
⇒x-1;y+1∈UC(5)={-1;1;-5;5}
⇒(1)$\left \{ {{x-1=1} \atop {y+1=5}} \right.$⇔ $\left \{ {{x=2} \atop {y=4}} \right.$
⇒(2)$\left \{ {{x-1=-1} \atop {y+1=-5}} \right.$⇔ $\left \{ {{x=0} \atop {y=-6}} \right.$
⇒(3)$\left \{ {{x-1=5} \atop {y+1=1}} \right.$⇔ $\left \{ {{x=6} \atop {y=0}} \right.$
⇒(4)$\left \{ {{x-1=-5} \atop {y+1=-1}} \right.$⇔ $\left \{ {{x=-4} \atop {y=-2}} \right.$
⇒(x;y)=(2;4); (0;-6); (6;0); (-4;-2)
b)2x(y-3)=-3
⇒2x; y-3∈UC(-3)={-1;1;-3;3}
⇒(1)$\left \{ {{2x=1} \atop {y-3=-3}} \right.$⇔ $\left \{ {{x=\frac{1}{2}} \atop {y=0}} \right.$(loại)
⇒(2) $\left \{ {{2x=-1} \atop {y-3=3}} \right.$⇔ $\left \{ {{x=\frac{-1}{2}} \atop {y=6}} \right.$ (loại)
⇒(3)$\left \{ {{2x=3} \atop {y-3=-1}} \right.$⇔ $\left \{ {{x=\frac{3}{2}} \atop {y=2}} \right.$ (loại)
⇒(4)$\left \{ {{2x=-3} \atop {y-3=1}} \right.$⇔ $\left \{ {{x=\frac{-3}{2}} \atop {y=4}} \right.$ (loại)
⇒Không có x,y
c)(x+2)(y-1)=3
⇒x+2; y-1∈UC(3)={-1;1;-3;3}
⇒(1)$\left \{ {{x+2=1} \atop {y-1=3}} \right.$⇔ $\left \{ {{x=-1} \atop {y=4}} \right.$
⇒(2)$\left \{ {{x+2=-1} \atop {y-1=-3}} \right.$⇔ $\left \{ {{x=-3} \atop {y=-2}} \right.$
⇒(3)$\left \{ {{x+2=3} \atop {y-1=1}} \right.$⇔ $\left \{ {{x=1} \atop {y=2}} \right.$
⇒(4)$\left \{ {{x+2=-3} \atop {y-1=-1}} \right.$⇔ $\left \{ {{x=-5} \atop {y=0}} \right.$
⇒(x;y)=(-1;4); (-3;-2); (1;2); (-5;0)
