Question

Determinati perechile de numere naturale x si y , astfel incat fractia  $\frac{10}{(x+10)*(y+2)}$ sa fie echiunitara .

Answer 1

[x+10]·[y+1]=10
⇒singura varianta posibila este
x+10=10
⇒x=10-10
⇒x=0;
y+1=1
⇒y=0;
⇒x,y∈[0];

Answer 2

[tex]10=2\cdot 5~~\text{sau}~~10=1\cdot 10. \\ \text{Ca~sa~fie~echiunitara}\Rightarrow (x+10)\cdot (y+2)=10. \\ \text{Daca}~(x+10)=5~si~(y+2)=2~\text{sau~invers~nu~sunt~solutii~a.i.:}~x,y\in \mathbb{N}} \\ \text{Daca}~(x+10)=10\Rightarrow \boxed{x=0;}~y+2=1\Rightarrow y\notin \mathbb{N}}. \\\\ \underline{In~concluzie,~nu~exista~x~si~y~cu~proprietatea~data.}[/tex]