Question

(2x-1)^9-(2x-1)^11=0

(2-3x)^13=(3x-2)^12

Answer 1

+) \(\left(2x-1\right)^9-\left(2x-1\right)^{11}=0\)

\(\Leftrightarrow\left(2x-1\right)^9=\left(2x-1\right)^{11}\)

\(\Leftrightarrow\orbr{\begin{cases}2x-1=0\\2x-1=1\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=1\end{cases}}}\)

+) \(\left(2-3x\right)^{13}=\left(3x-2\right)^{12}\)

\(\Leftrightarrow\left(2-3x\right)^{13}=\left(2-3x\right)^{12}\)

\(\Leftrightarrow\orbr{\begin{cases}2-3x=0\\2-3x=1\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{2}{3}\\x=\frac{1}{3}\end{cases}}\)