Question

tìm số nguyên x để x+1 chia hết cho 2x

Answer 1

\(x+1⋮2x\)

Mà \(2x⋮2x\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x+2⋮2x\\2x⋮2x\end{matrix}\right.\)

\(\Leftrightarrow2⋮2x\)

\(\Leftrightarrow2x\inƯ\left(2\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=1\\2x=2\\2x=-1\\2x=-2\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\\x=-\dfrac{1}{2}\\x=-1\end{matrix}\right.\)

Vậy ..

Answer 2

Ta có:

\(\dfrac{x+1}{2x}\Rightarrow x+1⋮2x\Rightarrow2x+2⋮2x\Leftrightarrow1⋮x\)

\(\Rightarrow x\inƯ\left(1\right)\)

\(\Rightarrow x\in\left\{1;-1\right\}\)

Vậy khi \(x\in\left\{1;-1\right\}\) thì x+1 chia hết cho 2x