Question

Tìm n e Z biết

A=\(\dfrac{n+7}{n+5}\) là số nguyên

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Answer 1

\(A=\dfrac{n+7}{n+5};A\in Z\)

\(\Leftrightarrow n+7⋮n+5\)

\(n+5+2⋮n+5\Rightarrow2⋮n+5\)

\(\Rightarrow n+5\inƯ\left(2\right)\)

\(Ư\left(2\right)=\left\{\pm1;\pm2\right\}\)

\(\Leftrightarrow n+5=1\Rightarrow n=-4\)

\(\Leftrightarrow n+5=-1\Rightarrow n=-6\)

\(\Leftrightarrow n+5=2\Rightarrow n=-3\)

\(\Leftrightarrow n+5=-2\Rightarrow n=-7\)

Answer 2

A =\(\dfrac{n+7}{n+5}\) là số nguyên

=> (n +7 ) \(⋮\)( n+5)

=> ( n + 5 + 2)\(⋮\) ( n+ 5)

=> 2 \(⋮\) ( n + 5)

=> n + 5 \(\in\) Ư( 2)

=> n + 5 \(\in\) { -2 ; -1 ; 1; 2 }

Vì n \(\in\) Z

=> n \(\in\) { -7;-6 ; -4 ; -3 }

Vậy :=> n \(\in\) { -7;-6 ; -4 ; -3 }