Question

\(A=-\dfrac{4}{2+x}\). Tìm x nguyên để A nguyên dương.

Answer 1

ĐK: \(2+x\ne0\Leftrightarrow x\ne-2\)

A nguyên dương \(\Leftrightarrow-\dfrac{4}{2+x}>0\)

Mà -4<0 nên để A>0 thì 2+x<0 <=> x<-2

Vậy khi x<-2 thì A nguyên dương.

Answer 2

Để `A in N**`

`=>A>0,A in N`

`A>0`

`=>-4/(x+2)>0`

`=>x+2<0`

`=>x<-2`

`A in N`

`=>-4 vdots x+2`

`=>x+2 in Ư(4)={+-1,+-2,+-4}`

`=>x in {-3,-1,0,-4,-6,2}`

Mà `x<-1`

`=>x in {-3,-,4,-6}`

Answer 3

Để A là số nguyên dương thì \(\left\{{}\begin{matrix}x+2< 0\\4⋮x+2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< -2\\x+2\in\left\{1;-1;2;-2;4;-4\right\}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x< -2\\x\in\left\{-1;-3;0;-4;2;-6\right\}\end{matrix}\right.\Leftrightarrow x\in\left\{-3;-4;-6\right\}\)