Question

C={x€N | 3X+2/2X+3 €N}

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Răspuns:

C = {1}

Explicație pas cu pas:

$\frac{3x + 2}{2x + 3}\in \mathbb{N}$

(2x + 3) divide pe (3x + 2) =>

$(2x + 3) \ \Big| \ (2x + 3) | \cdot 3 \implies \ (2x + 3) \ \Big| \ (6x + 9)\\ (2x + 3) \ \Big| \ (3x + 2) | \cdot 2 \implies (2x + 3) \ \Big| \ (6x + 4)$

=> (2x + 3) divide și diferența:

$(2x + 3) \ \Big| (6x + 9 - 6x - 4) \implies (2x + 3) \ \Big| 5 \\ \implies (2x + 3) \in \{1; 5\} \Big|_{-3} \implies 2x \in \{-2;2\} \Big|_{:2} \\ \implies x \in \{-1;1\} \cap \mathbb{N} \implies \bf x = 1$

=> C = {1}