Vì vế trái \(\left|x\left(x-4\right)\right|\ge0\)với mọi x nên vế phải \(x\ge0\) .
Ta có :
\(x.\left|x-4\right|=x\) ( vì \(x\ge0\) )
Nếu x = 0 thì 0.| 0 - 4 | = 0 ( đúng )
Nếu \(x\ne0\) thì ta có \(\left|x-4\right|=1\Leftrightarrow x-4=\pm1\Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\end{matrix}\right.\)
Vậy ta có x = 0 ; 3 ; 5
\(\left|x\left(x-4\right)\right|=x\)
\(\Rightarrow\left[{}\begin{matrix}x\left(x-4\right)=x\\x\left(x-4\right)=-x\end{matrix}\right.\)
+) \(x\left(x-4\right)=x\)
\(\Rightarrow x^2-4x-x=0\)
\(\Rightarrow x^2-5x=0\)
\(\Rightarrow x\left(x-5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x-5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)
+) \(x\left(x-4\right)=-x\)
\(\Rightarrow x^2-4x+x=0\)
\(\Rightarrow x^2-3x=0\)
\(\Rightarrow x\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
Vậy \(x\in\left\{0;3;5\right\}\)
