Question

Tìm x € Z biết 

X^2 + 2 chia hết cho x + 2

Ai làm được mình tick cho

Answer 1

Dễ thui

\(x^2+2=\left(x+2\right)\left(x+2\right)-4\left(x+2\right)-6\)

Suy ra \(6⋮\left(x+2\right)\)

Suy ra \(x+2\inƯ\left(6\right)=\left\{\pm1;\pm2;\pm3;\pm6\right\}\)

Vậy \(x\in\left\{-1;-3;0;-4;-5;1;4;-8\right\}\)

Hết.