Question

A={x∈Z| 9supra x-3 ∈Z} si
B{X∈Z|GDIVIZIBIL CU X  SAU    4 DIVIZIBIL CU X} 
DETERMINATI MULTIMILE.
                                                      

Answer 1

$\frac{9}{x-3}$ ∈ Z

x-3 divizibil cu 9
x-3=1,3,9,-1,-3,-9

x-3=1
x=4

x-3=3
x=6

x-3=9
x=12

x-3=-1
x=2

x-3=-3
x=0

x-3=-9
x=-6

A={4,6,12,2,0,6)

Answer 2

$A= \{ x \ apartine \ Z | \frac{9}{x-3} \ apartine \ Z \} \\ \\ \frac{9}{x-3} \ apartine \ Z => \ (x-3)|9 \ <=> x-3 = \{-1,1,-3,3,-9,9 \} \\ \\ 1)x-3= -1 =>x= 2 \\ \\ 2)x-3=1 => x= 4 \\ \\ 3) x-3=-3 =>x= 0 \\ \\ 4)x-3=3 =>x= 6 \\ \\ 5) x-3=-9 => x= -6 \\ \\ 6) x-3=9 =>x=12 \\ \\ \boxed{A= \{-6,0,2,4,6,12 \} }$

$B= \{x \ apartine \ Z | \ 4 |x \} => B= \{ -1; 1; -2; 2; -4;4 \}$