Question

cum se rezolva multimea: C={x∈N 3x+5/x-2 ∈N}

Answer 1

Notez $n=\dfrac{3x+5}{x-2}.$

$n=\dfrac{3(x-2)+11}{x-2}=3+\dfrac{11}{x-2} \\ \\ \Rightarrow (x-2)\in\{\pm 1;\pm 11\}$

Luăm toate cazurile:
$x-2=1\Rightarrow x=3 \Rightarrow n=14.$

$x-2=-1\Rightarrow x=1\Rightarrow n=-8\text{ (nu este natural)}$

$x-2=11\Rightarrow x=13 \Rightarrow n=4.$

$x-2=-11\Rightarrow x=-9\Rightarrow n=2.$

În concluzie, $x\in \{3,13,-9\}$