Question

[Ngô Hải Hà]

1.Tìm x

x+5 chia hết 2x-1

2.Tìm cặp số xy sao cho

xy-5x-3y+8=0

Answer 1

[Nguyễn Nam]

1) Ta có:

\(x+5⋮2x-1\)

\(\Rightarrow2\left(x+5\right)⋮2x-1\)

\(\Rightarrow2x+10⋮2x-1\)

\(\Rightarrow\left(2x-1\right)+11⋮2x-1\)

\(\Rightarrow11⋮2x-1\)

\(\Rightarrow2x-1\in U\left(11\right)=\left\{-1;1;-11;11\right\}\)

\(\Rightarrow\left\{{}\begin{matrix}2x-1=-1\Rightarrow x=0\\2x-1=1\Rightarrow x=1\\2x-1=-11\Rightarrow x=-5\\2x-1=11\Rightarrow x=6\end{matrix}\right.\)

Vậy \(x\in\left\{0;1;-5;6\right\}\)