Question

Fie multimile:
A={x apartine Z | 9/2x-5 apartine Z}
B={x apartine Z | 3x-7/2x+3 apartine Z}
Determinati A si B

Answer 1

Răspuns:

A={-2, 1, 2, 3, 4, 7} si B={-13,-2,-1,10}

Explicație pas cu pas:

9/2x-5 apartine lui Z=> 2x-5 = divizorii lui 9 care sunt: 1, 3 si 9 dar si -1, -3 si -9

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

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

2x-5=9 => 2x=14 => 7

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

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

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

Deci A={-2, 1, 2, 3, 4, 7}

(3x-7)/(2x+3) Z => (2x+3) | (3x-7) => (2x+3) | -2(3x-7) => (2x+3) | (-6x+14). ca (2x+3) | 3(2x+3),  (2x+3) | (6x+9)., (2x+3) | [(-6x+14)+(6x+9)] => (2x+3) | 23., 23  D_23={-1,1,-23,23}.Caz1: 2x+3=-1 => x=-2 Z;Caz2: 2x+3=1 => x=-1 Z;Caz3: 2x+3=-23 => x=-13  Z;Caz4: 2x+3=23 => x=10 Z;

Deci B={-13,-2,-1,10}