Question

Determină elementele mulțimii A={x€N | 14/2x+1€N}.Vă rog!​

Answer 1

$\frac{14}{2x + 1} \in\mathbb{N} \\ \\ \implies \: 2x + 1\in D _{ + 14} \\ \\ \implies \: 2x + 1\in\{1;2;7;14\} \\ \\ \implies \: 2x\in\{1 - 1;2 - 1;7 - 1;14 - 1\} \\ \\ \implies \: 2x\in\{0;1;6;15\} \\ \\ \implies \: x\in\{ \frac{0}{2} ; \frac{6}{2} \} \\ \\ \implies\boxed{ \: x\in\{0;3\}}$