Question

VA ROG MULT SA MA AJUTATI !! DAU COROANA !
Determinaţi perechile de numere naturale (a, b) pentru care are loc egalitatea \frac{ab}{a+2b} = \frac{3}{2}

Answer 1

[tex]\frac{ab}{a+2b}=\frac{3}{2}=\ \textgreater \ 2ab=3(a+2b) \\ Daca \ a=0 \ =\ \textgreater \ 0 = 6b =\ \textgreater \ b =0 =\ \textgreater \ (0,0) \\ Daca \ a=4 \ =\ \textgreater \ 8b = 3(4+2b) =\ \textgreater \ 8b = 12 + 6b =\ \textgreater \ 2b = 12 =\ \textgreater \ b = 6 \\ Daca \ a = 6 =\ \textgreater \ 12b = 3(2b+6) =\ \textgreater \ 12b = 6b+18 =\ \textgreater \ 6b = 18 =\ \textgreater \ \\ =\ \textgreater \ b = 3[/tex]
In concluzie, perechile sunt (0,0),(4,6) si (6,3).