Tìm x thuộc Z, biết |x-3| là Ư (6)

\(\left|x-3\right|\inƯ\left(6\right)\)

\(\Rightarrow\left|x-3\right|\in N\) (Vì \(\left|x-3\right|\) không thể là số nguyên)

\(\Rightarrow\left|x-3\right|=Ư\left(6\right)=\left\{1;2;3;6\right\}\)

\(\Rightarrow\left|x-3\right|=1\Rightarrow\left[\begin{matrix}x-3=1\\x-3=-1\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=4\\x=2\end{matrix}\right.\)

\(\Rightarrow\left|x-3\right|=2\Rightarrow\left[\begin{matrix}x-3=2\\x-3=-2\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=5\\x=1\end{matrix}\right.\)

\(\Rightarrow\left|x-3\right|=3\Rightarrow\left[\begin{matrix}x-3=3\\x-3=-3\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=6\\x=0\end{matrix}\right.\)

\(\Rightarrow x-3=6\Rightarrow\left[\begin{matrix}x-3=6\\x-3=-6\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=9\\x=-3\end{matrix}\right.\)

\(\Rightarrow x=\left\{-3;0;1;2;4;5;6;9\right\}\)