\(B=\dfrac{2n+15}{n+1}=\dfrac{2n+2+13}{n+1}=2+\dfrac{13}{n+1}\)
để \(\dfrac{2n+15}{n+1}\) \(\Leftrightarrow\dfrac{13}{n+1}\) nguyên \(\Leftrightarrow n+1\) là ước của \(13\) là \(\pm1;\pm2\)
ta có : * \(n+1=1\Leftrightarrow n=0\) (tmđk)
* \(n+1=-1\Leftrightarrow n=-2\) (tmđk)
* \(n+1=13\Leftrightarrow n=12\) (tmđk)
* \(n+1=-13\Leftrightarrow n=-14\) (tmđk)
vậy \(n=0;n=-2;n=12;n=-14\)
\(\dfrac{15}{n-2}\) nguyên \(\Leftrightarrow n-2\) là ước của \(15\) là \(\pm1;\pm3;\pm5;\pm15\)
ta có : * \(n-2=1\Leftrightarrow n=3\) (tmđk)
* \(n-2=-1\Leftrightarrow n=1\) (tmđk)
* \(n-2=3\Leftrightarrow n=5\) (tmđk)
* \(n-2=-3\Leftrightarrow n=-1\) (tmđk)
* \(n-2=5\Leftrightarrow n=7\) (tmđk)
* \(n-2=-5\Leftrightarrow n=-3\) (tmđk)
* \(n-2=15\Leftrightarrow n=17\) (tmđk)
* \(n-2=-15\Leftrightarrow n=-13\) (tmđk)
vậy \(n=3;n=1;n=5;n=-1;n=7;n=-3;n=17;n=-13\)
\(B=\dfrac{2n+15}{n+1}=\dfrac{2n+2+13}{n+1}=2+\dfrac{13}{n+1}\)
Để B đạt giá trị nguyên thì \(\dfrac{13}{n+1}\) phải đạt giá trị nguyên
\(\Rightarrow n+1\inƯ\left(13\right)\)
\(\Rightarrow n+1\in\left\{-13;-1;1;13\right\}\)
\(\Rightarrow n\in\left\{-14;-2;0;12\right\}\)
Vậy..................
\(A=\dfrac{15}{n-2}\)
Để A đạt giá trị nguyên thì \(\dfrac{15}{n-2}\) phải đạt giá trị nguyên
\(\Rightarrow n-2\inƯ\left(15\right)\)
\(\Rightarrow n-2\in\left\{-15;-5;-3;-1;1;3;5;15\right\}\)
\(\Rightarrow n\in\left\{-13;-3;-1;1;3;5;7;17\right\}\)
Chúc bạn học tốt!!!
\(B=\dfrac{2n+15}{n+1}=\dfrac{2n+2+13}{n+1}=\dfrac{2n+2}{n+1}+\dfrac{13}{n+1}=\dfrac{2\left(n+1\right)}{n+1}+\dfrac{13}{n+1}=2+\dfrac{13}{n+1}\)\(B\in Z\Rightarrow13⋮n+1\)
\(\Rightarrow n+1\in U\left(13\right)\)
\(U\left(13\right)=\left\{\pm1;\pm13\right\}\)
\(\Rightarrow\left\{{}\begin{matrix}n+1=1\Rightarrow n=0\\n+1=-1\Rightarrow n=-2\\n+1=13\Rightarrow n=12\\n+1=-13\Rightarrow n=-14\end{matrix}\right.\)
\(A=\dfrac{15}{n-2};A\in Z\Rightarrow15⋮n-2\)
\(\Rightarrow n-2\in U\left(15\right)\)
\(U\left(15\right)=\left\{\pm1;\pm3;\pm5;\pm15\right\}\)
\(\Rightarrow\left\{{}\begin{matrix}n-2=1\Rightarrow n=3\\n-2=-1\Rightarrow n=1\\n-2=3\Rightarrow n=5\\n-2=-3\Rightarrow n=-1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}n-2=5\Rightarrow n=7\\n-2=-5\Rightarrow n=-3\\n-2=15\Rightarrow n=17\\n-2=-15\Rightarrow n=-13\end{matrix}\right.\)
