Question

Determinati multimea A={x apartine Z|5\2x+1 apartine Z}. ​

Answer 1

Răspuns:

$A = \Big\{-3;-1;0;2\Big\}$

Explicație pas cu pas:

$\frac{5}{2x+1} \in \mathbb{Z} \implies 2x+1 \in D_5 \\ \\ 2x+1 = -5\iff 2x = -6 \iff x = -3\\ \\ 2x+1 = -1 \iff 2x = -2\iff x=-1\\ \\ 2x+1 = 1\iff 2x = 0\iff x = 0\\ \\ 2x+1 = 5 \iff 2x = 4\iff x = 2\\ \\ A = \Big\{-3;-1;0;2\Big\}$

Answer 2

D5={-1;-5;1;5}

2x+1=-1

2x=-1-1

2x=-2

x=-2/2

x=-1

2x+1=-5

2x=-5-1

2x=-6

x=-6/2

x=-3

2x+1=1

2x=1-1

2x=0

x=0

2x+1=5

2x=5-1

2x=4

x=4/2

x=2

A={-3;-1;0;2}