Question

[Liên Nguyễn]

Tìm x€Z 

x²-x+2 :hết cho x-1

Giúp mk với😙😙

Answer 1

[Huyền Nhi]

\(x^2-x+2⋮x-1\Leftrightarrow x\left(x-1\right)+2⋮x-1\)

Vì \(x\inℤ\Rightarrow x-1\inℤ\Rightarrow x\left(x-1\right)\inℤ\)

\(\Rightarrow x\left(x-1\right)+2⋮x-1\Leftrightarrow2⋮x-1\)

\(\Leftrightarrow x-1\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)

\(\Leftrightarrow x\in\left\{0;2;-1;3\right\}\)

Vậy x = ........................