Question

$\frac{4x + 23}{2x + 1}$
Aflați pe x care aparține nr Z. Rezolvare completa, vă rog!​

Answer 1

Răspuns:

sper ca am înțeles enunțul

Answer 2

Explicație pas cu pas:

$\dfrac{4x + 23}{2x + 1} \in \mathbb{Z} \ , \ x \in \mathbb{Z}$

$\dfrac{4x + 23}{2x + 1} = \dfrac{4x + 2 + 21}{2x + 1} = \dfrac{2(2x + 1) + 21}{2x + 1} = \\ = 2 + \dfrac{21}{2x + 1} \in \mathbb{Z} \iff \dfrac{21}{2x + 1} \in \mathbb{Z}$

$(2x + 1) \in D_{21} \iff (2x + 1) \in \{-21;-7;-3;-1;1;3;7;21\} \ \Big|-1$

$2x \in \{-22;-8;-4;-2;0;2;6;20\} \ \Big|:2$

$\implies x \in \{-11;-4;-2;-1;0;1;3;10\}$