\(\left(x-1\right)^2=\left(x-1\right)^4\)
\(\Rightarrow\left(x-1\right)^2-\left(x-1\right)^4=0\)
\(\Rightarrow\left(x-1\right)^2.1-\left(x-1\right)^2.\left(x-1\right)^2=0\)
\(\Rightarrow\left(x-1\right)^2.\left[\left(x-1\right)^2-1\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(x-1\right)^2=0\\\left(x-1\right)^2-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\\left(x-1-1\right)\left(x-1+1\right)=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=1\\x=2;x=0\end{cases}}}\)
Vậy: \(x\in\left\{1;2;0\right\}\)
(x - 1)2 = (x - 1)4
<=> (x - 1)2 - (x - 1)4 = 0
<=> (x - 1)2 - (x - 1)2.(x - 1)2 = 0
<=> (x - 1)2. [1 - (x - 1)2] = 0
<=> x - 1 = 0 hoặc 1 - (x - 1)2 = 0
<=> x = 1 <=> (x - 1)2 = 1
<=> x - 1 = 1 hoặc x - 1 = -1
<=> x = 2 <=> x = 0
Vậy x = 1; x = 2; x = 0
\(\left(x-1\right)^2=\left(x-1\right)^4\)
\(\Leftrightarrow\left(x-1\right)^2-\left(x-1\right)^4=0\)
\(\Leftrightarrow\left(x-1\right)^2\left[1-\left(x-1\right)^2\right]=0\)
\(\Leftrightarrow\left(x-1\right)^2\left(1-x+1\right)\left(1+x-1\right)=0\)
\(\Leftrightarrow x\left(x-1\right)^2\left(2-x\right)=0\Leftrightarrow x=0;x=1;x=2\)
Nếu \(\left(x-1\right)^2=0\Rightarrow x=1\left(tm\right)\)
Nếu \(\left(x-1\right)^2\ne0\Leftrightarrow\left(x-1\right)^2=1\Leftrightarrow\orbr{\begin{cases}x-1=1\\x-1=-1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\\x=0\end{cases}}\)
Vậy x = 0 hoặc x = 1 hoặc x = 2
