Question

8. Determinați x apartine N, care verifică relația (x+1)|(3x+11). ​

Answer 1

Explicație pas cu pas:

(x+1) | (3x+11)

$(x + 1) \in \mathbb{N} \implies x + 1 > 0 \implies 3x + 11 > 0$

$\dfrac{3x + 11}{x + 1} = \dfrac{3x + 3 + 8}{x + 1} = \dfrac{3(x + 1) + 8}{x + 1} = 3 + \dfrac{8}{x + 1} \\ \implies (x + 1) \in \mathcal{D}_{8} \iff (x + 1) \in \Big\{ 1; 2; 4; 8\Big\}$

$\implies x \in \Big\{ 0; 1; 3; 7\Big\}$