Đáp án:
$\text{Vậy (x;y) ∈ {(3,2);(1,4);(-3,0)}}$
Giải thích các bước giải:
$\text{Theo bài ra ta có:}$
$\text{x,y ∈ Z}$
$\text{⇒x-2, xy-1 ∈ Z}$
$\text{Ta có các TH sau:}$
$\text{TH1: }$
$\left \{ {{x-2=1} \atop {xy-1=5}} \right.$ ⇔ $\left \{ {{x=1+2} \atop {xy=5+1}} \right.$ ⇔ $\left \{ {{x=3} \atop {3y=6}} \right.$ ⇔ $\left \{ {{x=3} \atop {y=2}} \right.$$\text{(thỏa mãn)}$
$\text{TH2: }$
$\left \{ {{x-2=5} \atop {xy-1=1}} \right.$ ⇔ $\left \{ {{x=5+2} \atop {xy=1+1}} \right.$ ⇔ $\left \{ {{x=7} \atop {7y=2}} \right.$ ⇔ $\left \{ {{x=7} \atop {y=\frac{2}{7}}} \right.$$\text{(loại)}$
$\text{TH3:
$\left \{ {{x-2=-1} \atop {xy-1=-5}} \right.$ ⇔ $\left \{ {{x=-1+2} \atop {xy=-5+1}} \right.$ ⇔ $\left \{ {{x=1} \atop {y=-4}} \right.$ $\text{(thỏa mãn)}$
$\text{TH4:}$
$\left \{ {{x-2=-5} \atop {xy-1=-1}} \right.$ ⇔ $\left \{ {{x=-5+2} \atop {xy=-1+1}} \right.$ ⇔ $\left \{ {{x=-3} \atop {-3y=0}} \right.$⇔ $\left \{ {{x=-3} \atop {y=0}} \right.$ $\text{(thỏa mãn)}$
$\text{Vậy (x;y) ∈ {(3,2);(1,4);(-3,0)}}$
