a, Ta có :
\(\left|x-1\right|+\left|x-4\right|=3x\)
+) \(x>1\) có :
\(1-x+4-x=3x\)
\(\Leftrightarrow5-2x=3x\)
\(\Leftrightarrow5x=5\)
\(\Leftrightarrow x=1\left(loại\right)\)
+) Với \(1\le x\le4\) ta có :
\(x-1+4-x=3x\)
\(\Leftrightarrow3=3x\)
\(\Leftrightarrow1=x\left(tm\right)\)
+) \(x\ge4\) có :
\(x-1+x-4=3x\)
\(\Leftrightarrow2x-3x=5\)
\(\Leftrightarrow-x=5\)
\(\Leftrightarrow x=-5\)\(\left(loại\right)\)
Vậy ...
b/ \(\left|x\left(x-4\right)\right|=x\)
\(\Leftrightarrow\left[{}\begin{matrix}x\left(x-4\right)=x\\x\left(x-4\right)=-x\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=1\\x-4=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\end{matrix}\right.\)
Vậy ..
