Question

Tìm n thuộc Z biết :

2 - 4n : n - 1

Answer 1

Ta có : \(2-4n⋮n-1\Leftrightarrow2-4n⋮4\left(n-1\right)\Leftrightarrow2-4n⋮4n-4\)

\(\Rightarrow\left(4n-4\right)+\left(2-4n\right)⋮n-1\)

\(\Rightarrow4n+4+2-4n⋮n-1\Rightarrow6⋮n-1\)

\(\Rightarrow n-1\in\left\{\pm1;\pm2;\pm3;\pm6\right\}\Rightarrow n\in\left\{2;3;4;7;0;-1;-2;-5\right\}\)

Vậy ...

Answer 2

Rút gọn biểu thức ta được

Nếu \(\left\{\begin{matrix}\frac{2-4n}{n-1}\\2-\frac{4n}{n-1}\end{matrix}\right.\Rightarrow\left\{\begin{matrix}\frac{4n-2}{1-n}\\\frac{2n+2}{1-n}\end{matrix}\right.\)