\(\left|x-1\right|=\left|x-5\right|\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x-1=x-5\\x-1=5-x\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x-x=-5+1\\x+x=5+1\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}0x=-4\left(loại\right)\\x=3\left(nhận\right)\end{array}\right.\)
Vậy ........
Ta có :
\(\left|x-1\right|=\left|x-5\right|\)
\(\Rightarrow\left[\begin{array}{nghiempt}\left|x-1\right|=x-5\\\left|x-1\right|=5-x\end{array}\right.\)
(+) | x - 1 | = x - 5
Vì | x - 1| lớn hơn hoặc bằng 0
=> x - 5 lớn hơn hoặc bằng 0
=> x lớn hơn hoặc bằng 5
=> | x - 1 | = x - 1
\(\Rightarrow x-1=x-5\)
\(\Rightarrow0=-4\left(l\right)\)
(+) |x -1 | =5 - x
\(\Rightarrow\left[\begin{array}{nghiempt}x-1=5-x\\x-1=x-5\end{array}\right.\)
\(\Rightarrow x-1=5-x\)
\(\Rightarrow x=3\)
Vậy x=3