Question

Determinati multimea A = {x ap. Z | x = 2n-3/n+2, n ap. Z, n \ {-2}

Answer 1

Explicație pas cu pas:

x€Z

x=(2n-3)/(n+2)

=> (2n-3)/(n+2) €Z <=> n+2 | 2n-3

n+2|2n-3

n+2|n+2 => n+2|2n+4

Le scadem:

n+2|2n+4-2n+3 => n+2|7 => n+2€D7 in Z =>

n+2€{-7,-1,1,7} =>

n€{-9,-3,-1,5} => x€{3;9;-5;1}