Question

Fie multimile:
A={x apartine Z | 9/2x-5 apartine Z}
B={x apartine Z | 3x-7/2x+3 apartine Z}
Determinati A si B

Answer 1

A={x∈Z|9/2x-5∈Z}
9/2x-5∈Z⇒2x-5∈D9
                2x-5∈{1,3,9,-1,-3,-9}
                2x∈{6,8,14,4,2,-4}
                 x∈{3,4,7,2,1,-2}
A={3,4,7,2,1,-2}
B={x∈Z|3x-7/2x+3∈Z}
3x-7/2x+3∈Z
2x+3/2x+3⇒2x+3/6x+9
2x+3/2x-7⇒2x+3/6x-21
Le scadem: 2x+3/30⇒2x+3∈D30
                                2x+3∈{1,2,3,5,6,10,15,30,-1,-2,-3,-5,-6,-10,-15,-30}
                                2x∈{-2,-1,0,2,3,7,12,27,-4,-5,-8,-9,-13,-18,-33}
                               x∈{-1,0,1,6,-2,-4,-9}
B={-1,0,1,6,-2,-4,-9}