Question

determinati elmentele multimii A={x€Z/18/2x-1€Z} cât se poate de rapid și corect. Dau fundiță

Answer 1

A={x€Z/18/(2x-1) €Z}
18/(2x-1) ∈ Z ⇒ 2x-1 ∈ D18={-18,-9,-6,-3,-2,-1,1,2,3,6,9,18}

2x-1= -18 ⇒ x=-17/2
2x-1= -9 ⇒ x=-4
2x-1= -6 ⇒ x=-5/2
2x-1= -3 ⇒ x=-1
2x-1= -2 ⇒ x=-1/2
2x-1= -1 ⇒x=0
2x-1= 1 ⇒ x=1 
2x-1= 2 ⇒ x=3/2
2x-1= 3 ⇒ x=2
2x-1= 6 ⇒ x=7/2
2x-1= 9 ⇒ x=5
2x-1= 18 ⇒ x=19/2
     x∈ Z
       ↓
A={-4,-1,0,1,2,5}