Question

Tìm \(x\in z\)để A có giá trị nguyên

\(A=\frac{5x-2}{x-2}\)

Answer 1

\(A=\frac{5x-2}{x-2}=\frac{5x-10+8}{x-2}=\frac{5\left(x-2\right)+8}{x-2}=5+\frac{8}{x-2}\)

A nguyên khi \(\frac{8}{x-2}\) nguyên <=> 8 chia hết cho x-2

<=>\(x-2\inƯ\left(8\right)=\){-8;-4;-2;-1;1;2;4;8}

<=>\(x\in\){-6;-2;0;1;3;4;6;10}

Vậy ........