Question

Determinati multimea A ∩ B, unde:
A={n ∈ Z| 5n+14/2n-7 ∈ Z}

si B={n ∈Z| 5n-9/2n-9 ∈ Z}

Answer 1

Explicație pas cu pas:

5n+14/2n-7 €Z <=> 2n-7 | 5n+14 =>

2n-7 |2(5n+14)=> 2n-7|10n+28

2n-7|2n-7=> 2n-7|5(2n-7) => 2n-7|10n-35

Le scadem si avem

2n-7|10n+28-10n+35 => 2n-7|63 =>2n-7€D63 in Z =>

2n-7€{-63,-21,-9,-7,-3,-1,1,3,7,9,21,63} =>

2n€{-54,-14,-2,0,4,6,8,10,14,16,28,70} =>

n€{-27,-7,-1,0,2,3,4,5,7,8,14,35}