Question

Tìm x thuộc Z để A=\(\frac{1-2x}{x+3}\)thuộc Z.

Answer 1

\(A=\frac{1-2x}{x+3}=\frac{-2x+1}{x+3}=\frac{-2x-6+7}{x+3}=\frac{-2\left(x+3\right)+7}{x+3}=-2+\frac{7}{x+3}\)

Vì \(-2\inℤ\)\(\Rightarrow\)Để \(A\inℤ\)thì \(\frac{7}{x+3}\inℤ\)

\(\Rightarrow7⋮x+3\)\(\Rightarrow x+3\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)

\(\Rightarrow x\in\left\{-10;-4;-2;4\right\}\)

Vậy \(x\in\left\{-10;-4;-2;4\right\}\)

Answer 2

ĐK:\(x\ne-3\)

Với \(A=\frac{1-2X}{X+3}=\frac{-2x-6+7}{x+3}=\frac{-2+7}{x+3}\)

A nguyên <=>\(x+3\inƯ\left(7\right)\)\(\Rightarrow x\in\left\{1;-1;7;-7\right\}\)

Vậy...