Question

A= n+1/-n -2

Tim n thuoc Z A la so nguyen

Answer 1

\(A=\frac{n+1}{-n-2}\)

\(A=\frac{n+1}{n+1-2n-3}\)

\(A=1+\frac{1}{-2n-3}\)

\(A=1-\frac{1}{2n+3}\)

để A thuộc Z thì 2n+3 thuộc Ư(1)

=> 2n+3 thuộc Ư(1)

TH1: 2n+3=1<=> 2n = -2 <=> n= -1

TH2: 2n+3= -1 <=> 2n = -4 <=> n= -2 

vậy n thuộc {-1;-2}

Answer 2

\(A=\frac{n+1}{-n-2}\)

\(A=\frac{n+1}{n+1-2n-3}\)

\(A=1+\frac{1}{-2n-3}\)

\(A=1-\frac{1}{2n+3}\)

để \(A\in Z\)thì \(2n+3\inƯ\left(1\right)\)

\(\Leftrightarrow2n+3\in\left\{\pm1\right\}\)

+  \(2n+3=1\Leftrightarrow2n=-2\Leftrightarrow n=-1\)

+ \(2n+3=-1\Leftrightarrow2n=-4\Leftrightarrow n=-2\)

vậy...