Question

Aflati nr intreg x stiind ca 11supra2x-1 este nr intreg

Answer 1

[tex] \frac{11}{2x-1} eZ =\ \textgreater \ \\ (2x-1)eD _{11} ={-11,-1,1,11} \\ =\ \textgreater \ 2x-1=-11=\ \textgreater \ 2x=-10=\ \textgreater \ x=-5 \\ =\ \textgreater \ 2x-1=-1=\ \textgreater \ 2x=0=\ \textgreater \ x=0 \\ =\ \textgreater \ 2x-1=1=\ \textgreater \ 2x=2=\ \textgreater \ x=1 \\ =\ \textgreater \ 2x-1=11=\ \textgreater \ 2x=12=\ \textgreater \ x=6 \\ R: xe-5,0,1,6 \\ Succes! \\ e-apartine[/tex]

Answer 2

[tex]\frac{11}{2x-1} \in \mathbb{Z} \ \textless \ =\ \textgreater \ 2x-1 | 11 =\ \textgreater \ 2x-1 \in D_{11} =\ \textgreater \ \\ =\ \textgreater \ 2x-1 \in \{\pm 1, \pm 11 \}; \\ 2x-1=1=\ \textgreater \ 2x=2|:2 =\ \textgreater \ x = 1; \\ 2x-1=-1 =\ \textgreater \ 2x=0|:2=\ \textgreater \ x=0; \\ 2x-1=11=\ \textgreater \ 2x=12|:2=\ \textgreater \ x=6; \\ 2x-1=-11 =\ \textgreater \ 2x=-10|:2=\ \textgreater \ x=-5. \\ Semnul \ | \ inseamna \ "divide". \ Desigur, \ trebuie \ sa \ punem \ si \ conditia \\ de \ existenta, \ adica \ numitorul \ 2x-1 \neq 0 =\ \textgreater \ 2x \neq 1 =\ \textgreater \ x \neq \frac{1}{2} \in \mathbb{Q} \\ care\ nu \ este\ intreg\ , deci \ x \in \{-5,0,1,6\} \\ Succes \ la \ mate![/tex]