Explicație pas cu pas:
g)
[tex] \frac{2x - 3}{x + 5} = \frac{2x + 10 - 13}{x + 5} = \frac{2(x + 5) - 13}{x + 5} \\ = 2 - \frac{13}{x + 5} \\ 2\in \mathbb{Z} \iff \frac{13}{x + 5}\in \mathbb{Z} \\ (x + 5)\in\{ - 13 ; - 1 ;1;13\}[/tex]
[tex]x + 5 = - 13 = > x = - 18 \\ x + 5 = - 1 = > x = - 6 \\ x + 5 = 1 = > x = - 4 \\ x + 5 = 13 = > x = - 8[/tex]
=> G = {-18; -6; -4; -8}
h)
[tex]{x}^{2} + x = 2 \cdot (1\cdot2\cdot3...\cdot2021)[/tex]
[tex]x(x + 1) = 2 \cdot \frac{2021\cdot2022}{2} \\ x(x + 1) = 2021\cdot2022 \\ x \in \mathbb{N} \implies x = 2021[/tex]
