Question

( 2x + 1)^ 5= ( 2x+ 1) ^ 2011

Answer 1

\(\left(2x+1\right)^5=\left(2x+1\right)^{2011}\)

\(\Rightarrow\left(2x+1\right)^{2011}-\left(2x+1\right)^5=0\)

\(\Rightarrow\left(2x+1\right)^5\left[\left(2x+1\right)^{2006}-1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(2x+1\right)^5=0\\\left(2x+1\right)^{2006}-1=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x+1=0\\\left(2x+1\right)^{2006}=1\end{matrix}\right.\)

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

\(\Rightarrow\left[{}\begin{matrix}x=-0,5\\x=0\end{matrix}\right.\)