Determinați numerele naturale a si b pentru care.


a*b+3*a+2b=14

Va rog repede va dau coroana

a=3 si b=1

Verificare 3 x 1 + 3 x 3 + 2 x 1=14

3+9+2=14

[tex]\it ab+3a+2b=14|_{+6} \Rightarrow ab+3a+2b+6=20 \Rightarrow b(a+2)+3(a+2) =20\Rightarrow\\\\\Rightarrow (a+2)(b+3)=20 \ \ \ \ (1)\\\\a,b\in \mathbb{N} \Rightarrow a+2\geq2,\ b+3\geq3 \ \ \ \ (2)[/tex]

[tex]\it (1),(2) \Rightarrow (a+2,\ b+3) \in \{(2,10),\ (4,5),\ (5,4) \} \Rightarrow\\\\(a,b) \in \{(0,7),\ (2,2),\ (3,1) \}[/tex]