a)\(\left|x-1\right|+\left|\left(x-1\right)\left(x-2\right)\right|=0\)
\(pt\Leftrightarrow\left|x-1\right|\left(\left|x-2\right|+1\right)=0\)
Dễ thấy: \(\left|x-2\right|+1\ge1>0\) (loại)
\(\Rightarrow\left|x-1\right|=0\Rightarrow x-1=0\Rightarrow x=1\)
b)\(\left|x\right|+\left|y-1\right|+\left|z-3\right|=0\)
Dễ thấy: \(\left\{{}\begin{matrix}\left|x\right|\ge0\\\left|y-1\right|\ge0\\\left|z-3\right|\ge0\end{matrix}\right.\)
\(\Rightarrow\left|x\right|+\left|y-1\right|+\left|z-3\right|\ge0\)
Xảy ra khi \(\left\{{}\begin{matrix}\left|x\right|=0\\\left|y-1\right|=0\\\left|z-3\right|=0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=0\\y=1\\z=3\end{matrix}\right.\)
c)\(\left|x-1\right|=x-1\)
\(\Rightarrow\left[{}\begin{matrix}x-1=x-1\\x-1=1-x\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x\in R\\x=1\end{matrix}\right.\)
