\(\left|x\left(6-x\right)\right|=x\)
\(\Rightarrow\left\{{}\begin{matrix}x\left(6-x\right)=-x\\x\left(6-x\right)=x\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\left(6-x\right)+x=0\\x\left(6-x\right)-x=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x\left(6-x+1\right)=0\\x\left(6-x-1\right)=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\left(7-x\right)=0\\x\left(5-x\right)=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=0\\x=7\end{matrix}\right.\\\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\end{matrix}\right.\)
Vậy \(x\in\left\{0;5;7\right\}\)
Chúc bạn học tốt!!!
\(\text{1) |x(6−x)|=x}\)
=>\(x\left(6-x\right)=-x\)hoặc \(x\left(6-x\right)=x\)
=>\(x\left(6-x\right)+x=0\) hoặc \(x\left(6-x\right)-x=0\)
=>\(x\left(x+7\right)=0\) hoặc \(x\left(5-x\right)=0\)
=>x=0 hoặc x+7=0 hoặc x=0 hoặc 5-x=0
=>x=0 hoặc x=7 hoặc x=5
Vậy ....