Question

Tìm các số nguyên sao cho a^2 + a + 2 chia hết cho a+1

Answer 1

\(\Leftrightarrow a\left(a+1\right)+2⋮a+1\)

\(\Leftrightarrow a+1\in\left\{1;-1;2;-2\right\}\)

hay \(a\in\left\{0;-2;1;-3\right\}\)

Answer 2

\(a^2+a+2=a\left(a+1\right)+2\)

-Để \(a^2+a+2\) chia hết cho \(a+1\) thì \(2⋮\left(a+1\right)\)

\(\Rightarrow a+1\inƯ\left(2\right)\)

\(\Rightarrow a+1\in\left\{1;-1;2;-2\right\}\)

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