Question

va rog ajutati-ma cu exercitiul din poza
!

Answer 1

a)A={x∈Z | 9/(2x-5)∈Z }

9/(2x-5) ∈Z  
x∈Z                   =>(2x-5)|9  =>(2x-5)={-1;1-3;3;-9;9}

1)2x-5= -1 <=> 2x= 4 =>x=2

2)2x-5= 1 <=> 2x= 6 =>x=3

3)2x-5= -3 <=> 2x= 2 =>x=1

4)2x-5= 3 <=> 2x= 8 =>x=4

5)2x-5=-9 <=> 2x= -4 =>x= -2

6)2x-5= 9 <=> 2x= 14 =>x=7

A={-2;1;2;3;4;7}

B={x∈Z | (3x-7)/(2x+3) ∈ Z}

(3x-7)/(2x+3) ∈Z
x∈Z                        =>

=>(2x+3)|(3x-7)  |2
    (2x+3)|(2x+3) |3   <=>

<=> (2x+3)|2(3x-7)
       (2x+3)|3(2x+3)  <=>

<=>(2x+3)|(6x-14)
      (2x+3)|(6x+9)  <=>   (2x+3)|6x+9-6x+14   <=> (2x+3)|23  =>

=>(2x+3)={-1;1;-23;23}

1)2x+3 =1 <=> 2x=-2 => x= -1

2)2x+3= -1 <=> 2x= -4 =>x= -2

3)2x+3= -23 <=> 2x= -26 =>x= -13

4)2x+3= 23 <=> 2x= 20 =>x=10

B={-23;-2;-1;10}

A intersectat B ={-2}

A U B={-23;-2;-1;1,2,3,4,7,10}
B \ A ={-23;-1;10}

A \ B ={1,2,3,4,7}