Question

Tìm số nguyên m để A = \(\dfrac{m^2+m+2}{2\left(m+1\right)}\) nhận giá trị nguyện

Answer 1

\(A=\dfrac{m^2+m+2}{2\left(m+1\right)}=\dfrac{m\left(m+1\right)+2}{2\left(m+1\right)}=\dfrac{m\left(m+1\right)}{2\left(m+1\right)}+\dfrac{2}{m+1}\)

Để \(A\in Z\) thì \(\dfrac{m\left(m+1\right)}{2\left(m+1\right)}+\dfrac{2}{m+1}\in Z\)

Mà \(m\left(m+1\right)⋮2\left(m+1\right)\) nên \(2⋮m+1\)

\(\Rightarrow m+1\inƯ\left(2\right)=\left\{1;-1;2;-2\right\}\)

\(\Rightarrow m\in\left\{0;-2;1;-3\right\}\)