Question

sa se determine elementele multimii A={x€ Z| 5/2x-1 €Z}
( € inseamna apartine )
repede v a rog frumosss
dau coroanaaa la primul

Answer 1

  
[tex]\displaystyle\\ \frac{5}{2x-1} \in Z\\\\ \Longrightarrow (2x-1) \in D_{5Z}\\\\ D_{5z}=\{-5;~-1;~1;~5\}\\\\ 2x - 1 = -5 \Longrightarrow 2x = -5+1\Longrightarrow x= \frac{-5+1}{2}=\boxed{-2}\\\\ 2x - 1 = -1 \Longrightarrow 2x = -1+1\Longrightarrow x= \frac{-1+1}{2}=\boxed{0}\\\\ 2x - 1 = 1 \Longrightarrow 2x = 1+1\Longrightarrow x= \frac{1+1}{2}=\boxed{1}\\\\ 2x - 1 = 5 \Longrightarrow 2x = 5+1\Longrightarrow x= \frac{5+1}{2}=\boxed{3}\\\\ \Longrightarrow ~~\boxed{A=\{-2;~0;~1;~3\}}[/tex]