Question

Aflati x si y numere intregi pentru care xy+2x-3y=16

Answer 1

xy+2x-3y=16
x(y+2)=16+3y
x=(16+3y)/(y+2)
x=(3y+16)/(y+2)=(3y+6)/(y+2)+10/(y+2)=3+10/(y+2)∈Z
⇔ y+2 ∈ D10
y+2 ∈ {1,2,5,10,-1,-2,-5,-10}
y+2=1 ⇒y=-1 ⇒x=13
y+2=2 ⇒y=0 ⇒x=8
y+2=5 ⇒y=3 ⇒x=5
y+2=10 ⇒y=8 ⇒x=4
y+2=-1 ⇒y=-3 ⇒x=-7
y+2=-2 ⇒y=-4 ⇒x=-2
y+2=-5 ⇒y=-7 ⇒x=-1
y+2=-10 ⇒y=-12 ⇒x=2