Question

Determinati multimea:B={x/x€N si (x-5)/(3x+18)}
VA ROG AJUTOR REPEDE SUNT IN TEST​

Answer 1

Explicație pas cu pas:

(x-5) îl divide pe (3x+18)

$\dfrac{3x + 18}{x - 5} = \dfrac{3(x - 5) + 33}{x - 5} = 3 + \dfrac{33}{x - 5} \in \mathbb{Z} \\ \implies \dfrac{33}{x - 5} \in \mathbb{Z} \implies (x - 5) \in \mathcal{D}_{33}$

$x \geqslant 0 \implies x - 5 \geqslant - 5 \\ \mathcal{D}_{33} = \Big\{- 33; - 11; - 3; - 1; 1; 3; 11; 33\Big\} \\ \implies (x - 5) \in \Big\{- 3; - 1; 1; 3; 11; 33\Big\}$

$\implies (x - 5) \in \Big\{2; 4; 6; 8; 16; 38\Big\}$