Question

determinati mjltimea A={x€Z|7/2x+3€Z}​

Answer 1

Răspuns:

Explicație pas cu pas:

2x + 3 trebuie sa fie divizor al lui 7

2x + 3 = -1; 1; -7; 7

2x + 3 = -1

2x = -1-3 = -4

x = -4/2 = -2

__________

2x + 3 = 1

2x = 1 - 3 = -2

x = -2/2 = -1

___________

2x + 3 = -7

2x = -3 - 7 = -10

x = -10/2 = -5

___________

2x + 3 = 7

2x = 7 - 3 = 4

x = 4/2 = 2

____________

A = {-5; -2; -1; 2}

Answer 2

$\it \dfrac{7}{2x+3}\in\mathbb{Z}\ \Rightarrow\ 2x+3|7\ \Rightarrow\ 2x+3\in D_7\ \Rightarrow\ 2x+3\in\{\pm1,\ \pm7\}\ \Rightarrow\ \\ \\\Rightarrow\ 2x+3\in\{-7,\ -1,\ 1,\ 7\}|_{-3}\ \Rightarrow\ 2x\in\{-10,\ -4,\ -2,\ 4\}|_{:2}\ \Rightarrow\ \\ \\\Rightarrow\ x\in\{-5,\ -2,\ -1,\ 2\}$