Question

\((2\cdot x+1)^4=(2\cdot x+1)^6\)

Answer 1

\(\left(2x+1\right)^4=\left(2x+1\right)^6\)

=>\(\left(2x+1\right)^6-\left(2x+1\right)^4=0\)

=>\(\left(2x+1\right)^4\left[\left(2x+1\right)^2-1\right]=0\)

=>\(\left(2x+1\right)^4\cdot\left(2x+1-1\right)\left(2x+1+1\right)=0\)

=>\(2x\left(2x+1\right)^4\cdot\left(2x+2\right)=0\)

=>\(\left[{}\begin{matrix}2x=0\\\left(2x+1\right)^4=0\\2x+2=0\end{matrix}\right.\)

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