Question

Determinați perechile ( x, y ) de numere întregi nenule pentru care 2xy+3x-2y=12

Answer 1

$Hai~s-o~facem~din~nou:\\ \\ 2xy+3x-2y=12,~x,y\in~Z.\\ \\ x(2y+3)=12+2y~\Rightarrow~x=\frac{2y+12}{2y+3} \in~Z.\\ \\ \Rightarrow~\left \{ {{(2y+3)~|~(2y+3)} \atop {~(2y+3)~|~(2y+12)}} \right.~\Leftrightarrow~(2y+3)~|~9~\Leftrightarrow~2y+3\in~D_9=\{1,-1,3,-3,9,-9\}\\ \\ Dupa~ce~egalezi~pe~2y+3~cu~fiecare~termen~dintre~paranteze,~vei~avea:\\ \\ y=\{-1,-2,0,-3,3,-6\}\\ \\ x=\{10,-8,4,-2,2,0\}$