Question

(x-1)¹⁰=x-1

 

Answer 1

\(\left(x-1\right)^{10}=\left(x-1\right)\)

\(\Rightarrow\left(x-1\right)^{10}-\left(x-1\right)=0\)

\(\Rightarrow\left(x-1\right)\left[\left(x-1\right)^9-1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}x-1=0\\\left(x-1\right)^9-1=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=1\\\left(x-1\right)^9=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=1\\x-1=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=1\\x=1-1=0\end{matrix}\right.\)

Answer 2

\(\Leftrightarrow\left(x-1\right)\left[\left(x-1\right)^9-1\right]=0\)

=>x-1=0 hoặc x-1=1

=>x=1 hoặc x=2