Question

Determinati x din Z stiind ca
$\frac{13}{2x-1}$
-mie mi-a dat ca x=7 proba: $\frac{13}{2\cdot7-1}=\boxed1$ care apartine lui Z

Answer 1

$\frac{13}{2x-1} \in Z \Rightarrow 2x-1~|~13 \Rightarrow~(2x-1) \in D_{13} = \{ -13;~-1;~1;~13 \}. \\ \\ 2x-1=-13 \Rightarrow \boxed{x=-6 }~. \\ \\ 2x-1=-1 \Rightarrow \boxed{x=0}~. \\ \\ 2x-1=1 \Rightarrow \boxed{x=1}~. \\ \\ 2x-1=13 \Rightarrow \boxed{x=7}~. \\ \\ \underline{Solutie}:~x \in \{-6;0;1;7\}.$