Răspuns :

Dianageorgiana794id

Răspuns:

9/(2n+1)

2n+1 ∈ multimii divizorilor lui 9

D₉={1,3,9}

2n+1=1=>2n=1-1 =>n=0:2=>n=0

2n+1=3=>2n=3-1 =>n=2:2=>n=1

2n+1=9=>2n=9-1=>n=8:2=>n=4

n=0,1,4

Răspuns: [tex]\color{red}\LARGE\bf \boxed{ \bf n \in \{0;1;4\}}[/tex]

Explicație pas cu pas:

[tex]\large\bf \dfrac{9}{2n+1} \in \mathbb{N}\implies (2n+1) \in D_{9}[/tex]

[tex]\large\bf (2n+1) \in \{1,3,9\}~~~\bigg|-1[/tex]

[tex]\large\bf (2n+1 -1) \in \{1-1;3-1;9-1\}[/tex]

[tex]\large\bf 2n \in \{0;2;8\}~~~\bigg|:2[/tex]

[tex]\color{red}\LARGE\bf \boxed{ \bf n \in \{0;1;4\}}[/tex]

==pav38==

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