Đặt: \(a=x-1\Rightarrow x-2=a-1\)
Ta có:
\(a^4+\left(a-1\right)^4=1\)
\(\Leftrightarrow a^4+a^4-4a^3+6a^2-4a+1=1\)
\(\Leftrightarrow2a^4-4a^3+6a^2-4a=0\)
\(\Leftrightarrow a\left(2a^3-4a^2+6a-4\right)=0\)
\(\Leftrightarrow a\left(2a^3-2a^2-2a^2+2a+4a-4\right)=0\)
\(\Leftrightarrow a\left[2a^2\left(a-1\right)-2a\left(a-1\right)+4\left(a-1\right)\right]=0\)
\(\Leftrightarrow a\left(a-1\right)\left(2a^2-2a+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=0\\a=1\\2a^2-2a+4=2\left(a-\dfrac{1}{2}\right)^2+\dfrac{7}{2}=0\left(l\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-1=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
