Question

determinati toate numerele intredi (ab) astfel incat a/7=2/2b+1

Answer 1

[tex]\dfrac{a}{7}=\dfrac{2}{2b+1}\\ a\cdot (2b+1)=14\\ \text{De aici se deduc mai multe cazuri :}\\ \left \{ {{a=1} \atop {2b+1=14}} \right. \Leftrightarrow \left \{ {{a=1} \atop {b=\frac{13}{2}}\notin \mathbb{N}(\text{nu convine})} \right. \\ \\ \left \{ {{a=2} \atop {2b+1=7}} \right. \Leftrightarrow \left \{ {{a=2} \atop {b=3}} \right. \\ \\ \left \{ {{a=7} \atop {2b+1=2}} \right. \Leftrightarrow \left \{ {{a=7} \atop {b=\frac{1}{2}\notin \mathbb{N}(\text{nu convine})}} \right. \\ [/tex]

[tex] \left \{ {{a=14} \atop {2b+1=1}} \right.\\ \text{Nici aceasta nu convine,deoarece a trebuie sa fie o cifra.}\\ \text{Singura solutie este:}\\ S:\overline{ab}=23 [/tex]