Question

tìm số nguyên x để x^2+2/x+2 có giá trị nguyên

Answer 1

\(\Leftrightarrow x+2\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

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

Answer 2

\(\dfrac{x^2+2}{x+2}=\dfrac{x^2+2x-2x-4+6}{x+2}=\dfrac{x\left(x+2\right)-2\left(x+2\right)+6}{x+2}\\ =x-2+\dfrac{6}{x+2}\in Z\\ \Leftrightarrow x+2\inƯ\left(6\right)=\left\{-6;-3;-2;-1;1;2;3;6\right\}\\ \Leftrightarrow x\in\left\{-8;-5;-4;-3;-1;0;1;4\right\}\left(tm\right)\)