\(\left(x-25\right)^4=\left(x-25\right)^2\\ \Rightarrow\left(x-25\right)^4-\left(x-25\right)^2=0\\ \Rightarrow\left(x-25\right)^2\left[\left(x-25\right)^2-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}\left(x-25\right)^2=0\\\left(x-25\right)^2-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x-25=0\\\left(x-25\right)^2=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=25\\x-25=-1\\x-25=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=25\\x=24\\x=26\end{matrix}\right.\)
Ta có: \(\left(x-25\right)^4-\left(x-25\right)^2=0\)
\(\Rightarrow\left(x-25\right)^2\left[\left(x-25\right)^2-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-25\right)^2=0\\\left(x-25\right)^2-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=25\\\left[{}\begin{matrix}x=24\\x=26\end{matrix}\right.\end{matrix}\right.\)
\(\left(x-25\right)^4-\left(x-25\right)^2=0\Leftrightarrow\left(x-25\right)^2\left[\left(x-25\right)^2-1\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-25=0\\x-25=1\\x-25=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=25\\x=26\\x=24\end{matrix}\right.\)
=> \(\left(x-25\right)\left(x-25\right)^3-\left(x-25\right)\left(x-25\right)=0\)
<=> \(\left(x-25\right)\left(\left(x-25\right)^3-\left(x-25\right)\right)=0\)
\(< =>\left(x-25\right)\left(x^3-3.x^2.25+3.x.25^2-25^3-x+25\right)=0\)
<=> \(\left(x-25\right)\left(x^3-75x^2+1875x^2-15625-x+25\right)=0\)
<=> \(\left(x-25\right)\left(x^3+1800x^2-x-15600\right)=0\)
=> x = 25
