Question

Determina valorile intregi ale lui x pt. Care 2x-1|4x-15

Answer 1

x∈Z
2x-1I4x-15
2x-1I2x-1
2x-1I2*(2x-1)
2x-1I4x-2
2x-1I(4x-2)-(4x-15)
2x-1I13
2x-1∈D13
D13=1;-1;13;-13
Avem de analizat 4 cazuri
Cazul 1:
2x-1=1
2x=1+1
2x=2
x=2:2
x=1∈Z
Cazul 2:
2x-1=-1
2x=-1+1
2x=0
x=0:2
x=0∈Z
Cazul 3:
2x-1=13
2x=13+1
2x=14
x=14:2
x=7∈Z
Cazul 4:
2x-1=-13
2x=-13+1
2x=-12
x=-12:2
x=-6∈Z
In concluzie:
{x}={1;0;7;-6}