Question

Bài 1: Tìm các số nguyên x,y thỏa mãn pt: (2x+1)y=x+1

Answer 1

Lời giải:
Vì \(x\in\mathbb{Z}\Rightarrow 2x+1\neq 0\)

Ta có: \((2x+1)y=x+1\Rightarrow y=\frac{x+1}{2x+1}\)

Vì \(y\in\mathbb{Z}\Rightarrow \frac{x+1}{2x+1}\in\mathbb{Z}\)

\(\Leftrightarrow x+1\vdots 2x+1\)

\(\Rightarrow 2(x+1)\vdots 2x+1\)

\(\Rightarrow 2x+1+1\vdots 2x+1\Rightarrow 1\vdots 2x+1\)

Vậy \(2x+1\in\left\{\pm 1\right\}\Rightarrow x\in\left\{0;-1\right\}\)

+) \(x=0\Rightarrow y=1\)

+) \(x=-1\Rightarrow y=0\)

Vậy.................