Question

(2x-1)mũ 6 =(2x-1)mũ 8

 

Answer 1

\(\left(2x-1\right)^6=\left(2x-1\right)^8\\ \Rightarrow\left(2x-1\right)^6-\left(2x-1\right)^8=0\\ \Rightarrow\left(2x-1\right)^6\left[1-\left(2x-1\right)^2\right]=0\\ \Rightarrow\left[{}\begin{matrix}2x-1=0\\\left(2x-1\right)^2=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\2x-1=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\end{matrix}\right.\)

Answer 2

\(\left(2x-1\right)^6=\left(2x-1\right)^8\)

\(\Rightarrow\left[{}\begin{matrix}2x-1=-1\\2x-1=1\\2x-1=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\\x=\dfrac{1}{2}\end{matrix}\right.\)