Question

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

Answer 1

(2x+1)⁵=(2x+1)²⁰¹¹\(\Leftrightarrow\)(2x+1)⁵-(2x+1)²⁰¹¹=0

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

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

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

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