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Andramistoca13
a fost răspuns

Pentru ce valori intregi ale lui n numarul n2 + 4 / n este intreg ?
URGENT

Răspuns :

[tex]\frac{n^2+4}{n}=n+\frac{4}{n}\in Z\\ n|4\\ n\in \{-4,-2,-1,1,2,4\} [/tex]
   
[tex]\displaystyle\\ n \in Z\\\\ \frac{n^2+4}{n} \in Z\\\\ \frac{n^2+4}{n} = \frac{n^2}{n}+ \frac{4}{n}= \boxed{n+ \frac{4}{n}}\\\\ n \in N \\\\ \frac{4}{n} \in N ~~\text{daca}~~ n\in \text{multimii divizorilor intregi ai lui 4.}\\\\ D_4 = \{-4;~-2;~-1;~1;~2;~4\}\\\\ \Longrightarrow~~~\boxed{\bf n \in \{-4;~-2;~-1;~1;~2;~4\} }[/tex]