Răspuns :
Răspuns: [tex]\pink{\large \bf S \big\{(x,y)\big\} \in \Big\{\big(14,0 \big);\big(4,10 \big)\Big\}}[/tex]
Explicație pas cu pas:
11 este număr prim nu se descompune in alte numere, așadar îl putem scrie de 11 = 11 · 1
[tex]\large \bf (x-3)\cdot(y+1) = 11 \cdot 1[/tex]
[tex]\large \bf (x-3)\cdot(y+1) = 11 \implies[/tex]
- [tex]\text{\bf Caz 1}[/tex]
[tex]\large \bf x-3 = 1 \implies x=1+3\implies \boxed{\bf x = 4~\in \mathbb{Z}}[/tex]
[tex]\large \bf y+1 = 11 \implies y=11-1\implies \boxed{\bf y = 10~\in \mathbb{Z}}[/tex]
- [tex]\text{\bf Caz 2}[/tex]
[tex]\large \bf x-3 = 11 \implies x=11+3\implies \boxed{\bf x = 14~\in \mathbb{Z}}[/tex]
[tex]\large \bf y+1 = 1 \implies y=1-1\implies \boxed{\bf y = 0~\in \mathbb{Z}}[/tex]
[tex]\pink{\large \bf S \big\{(x,y)\big\} \in \Big\{\big(14,0 \big);\big(4,10 \big)\Big\}}[/tex]
#copaveibrainly