Question

tim n thuoc N sao cho cac p/so sau co gia tri la so nguyen :

9/n-1                                                             n/n-3

lam nhanh nhe ban minh cho like...................

Answer 1

                  Giải

+) Để \(\frac{9}{n-1}\inℤ\) thì \(9⋮\left(n-1\right)\)

\(\Leftrightarrow n-1\inƯ\left(9\right)=\left\{\pm1;\pm3;\pm9\right\}\)

Ta có bảng sau :

\(n-1\)	\(1\)	\(-1\)	\(3\)	\(-3\)	\(9\)	\(-9\)
\(n\)	\(2\)	\(0\)	\(4\)	\(-2\)	\(10\)	\(-8\)

\(\Rightarrow\) \(n\in\left\{-8;-2;0;2;4;10\right\}\)

Mà \(n\inℕ\) nên \(n\in\left\{0;2;4;10\right\}\)

+) Để \(\frac{n}{n-3}\inℤ\) thì \(n⋮\left(n-3\right)\)

\(\Leftrightarrow\left(n-3+3\right)⋮\left(n-3\right)\)

Vì \(\left(n-3\right)⋮\left(n-3\right)\) nên \(3⋮\left(n-3\right)\)

\(\Leftrightarrow n-3\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

Ta có bảng sau :

\(n-3\)	\(1\)	\(-1\)	\(3\)	\(-3\)
\(n\)	\(4\)	\(2\)	\(6\)	\(0\)

Vậy \(n\in\left\{0;2;4;6\right\}\)