Question

AFLATI X APARTINE Z DACA (2x-5)/(3x+2).

Answer 1

x∈Z
2x-5 I 3x+2
2x-5 I 2*(3x+2)
2x-5 I 6x+4
2x-5 I 2x-5
2x-5 I 3*(2x-5)
2x-5 I 6x-15
2x-5 I (6x+4)-(6x-15)
2x-5 I 19
2x-5∈D19
D19=1;-1;-19;19
Avem de analizat 4 cazuri:
Cazul 1:
2x-5=1
2x=6
x=3∈Z
Cazul 2:
2x-5=-1
2x=4
x=2∈Z
Cazul 3:
2x-5=-19
2x=-14
x=-7∈Z
Cazul 4:
2x-5=19
2x=24
x=12∈Z
In concluzie:
{x}={3;2;-7;12}