Question

Determinati numerele intregi x, stiind ca $\frac{11}{2x-1}$ este numar intreg.

Answer 1

$\frac{11}{2x-1}$ este intreg ⇒ $2x-1|11$ ⇒ $2x-1 ->D _{11}$ ⇒ $2x-1= {{ -11,-1, 1, 11 } \hbox { /+1}$

$2x=2,12,-10,0 \hbox { /\div2 }$

$\boxed {x=1,6,-5,0}$

Answer 2

2x-1I11
2x-1∈D11
2x-1∈{-11, -1,1,11}
2x-1=-11⇒2x=-11+1⇒x=-10/2⇒x=-5
2x-1=-1⇒2x=1-1⇒x=0
2x-1=1⇒2x=1+1⇒x=2/2⇒x=1
2x-1=11⇒2x=11+1⇒x=12/2⇒x=6
x∈{-5,0,1,6}