Question

xy+x-2y=3
Det x și y. X,y€Z
Help! Dau coronița!!✋

Answer 1

xy+x-2y=3⇒xy+x-2y-3=0⇒xy+x-2y-2-1=0⇒x(y+1)-2(y+1)=1⇒(x-2)(y+1)=1
caz1:x-2=1⇒x=1+2=3
         y+1=1⇒y=1-1=0
caz2:x-2=-1⇒x=-1+2=1
         y+1=-1⇒y=-1-1=-2

Answer 2

xy+x-2y = 3
x(y+1)-2y = 3
x(y+1) = 3+2y
x = (3+2y)/(y+1)
x = (2y+2+1)/(y+1) = (2y+2)/(y+1) + 1/(y+1) = 2(y+1)/(y+1) + 1/(y+1) = 
= 2 + 1/(y+1) ∈ Z

Cazul 1:
y+1 = -1 => y = -2 => x = 2 + 1/(-1) => x = 2-1 => x = 1

Cazul 2:
y+1 = 1 => y = 0 => x = 2 + 1/1 => x = 2+1 => x = 3

=> Solutiile sunt (x=1, y=-2), (x=3, y =0).