Question

Determinati perechile de numere naturale x si y , astfel incat fractia
[tex]\frac{(x+1)*(y+2)} sa fie echiunitara .

Answer 1

$10=2\cdot 5~~\text{sau}~~10=1\cdot 10. \\ \text{Ca~sa~fie~echiunitara}\Rightarrow (x+1)\cdot (y+2)=10. \\ \text{Daca}~(x+1)=5~\text{si}~(y+2)=2\Rightarrow \boxed{x=4;}~\boxed{y=0}\\\text{Daca}~(x+1)=2\Rightarrow \boxed{x=1;}~(y+2)=5\Rightarrow \boxed{y=3.}\\\text{Daca}~(x+1)=10\Rightarrow (y+2)=1~\Rightarrow~y\notin N.\\\text{Daca}~(x+1)=1\Rightarrow \boxed{x=0;}~(y+2)=10\Rightarrow \boxed{y=8.}$