Question

Aflati numerele naturale x pentru care: 3x+2 | 5x+6

Answer 1

Răspuns:

0 si 2

Explicație pas cu pas:

3x+2 | 5x+6 <=> (3x+2) | 3*(5x+6)

(3x+2) | (15x+18) <=> (3x+2) | [5*(3x+2)+8]

(3x+2) | 5*(3x+2) => (3x+2) | 8

$\implies (3x+2) \in \mathcal D_{8} \iff (3x+2) \in \{1;2;4;8\} \ \ \Big|-2$

$3x \in \{-1;0;2;6\} \ \ \Big|:3 \iff x \in \Big\{-\dfrac{1}{3} ;0;\dfrac{1}{3};2\Big\}$

$x \in \mathbb{N} \implies x \in \Big\{0;2\Big\}$