x∈Z
11/(2x-1)∈Z
2x-1I11
2x-1∈D11
D11={1;-1;11;-11}
Avem de analizat 4 cazuri:
Cazul 1:
2x-1=1
2x=2
x=1∈Z
Cazul 2:
2x-1=-1
2x=0
x=0∈Z
Cazul 3:
2x-1=11
2x=12
x=6∈Z
Cazul 4:
2x-1=-11
2x=-10
x=-5∈Z
In concluzie:
{x}={1;0;6;-5}
Proba:
11/(1*2-1)=11/1=11∈Z
11/(0*2-1)=11/-1=-11∈Z
11/(6*2-1)=11/11=1∈Z
11/(-5*2-1)=11/-11=-1∈Z
