\(\left(3y-1\right)^{10}=\left(3y-1\right)^{20}\)
\(3y-1=\left(3y-1\right)^2\)
\(\left(3y-1\right).1=\left(3y-1\right)\left(3y-1\right)\)
\(\Rightarrow3y-1=1\)
\(\Rightarrow3y=2\)
\(\Rightarrow y=\frac{2}{3}\)
trình bày chi tiết như ban kayasaru là sai
\(\left(3y-1\right)^{10}=\left(3y-1\right)^{20}\)
\(\Rightarrow\left(3y-1\right)^{10}-\left(3y-1\right)^{20}=0\)
\(\Rightarrow\left(3y-1\right)^{10}\times\left[1-\left(3y-1\right)^{10}\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(3y-1\right)^{10}=0\\1-\left(3y-1\right)^{10}=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}3y-1=0\\\left(3y-1\right)^{10}=1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}3y=1\\\left(3y-1\right)^{10}=\orbr{\begin{cases}1^{10}\\\left(-1\right)^{10}\end{cases}}\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}y=\frac{1}{3}\\y=\frac{2}{3}\\y=0\end{cases}}\)
kết luận:\(\hept{\begin{cases}y=\frac{1}{3}\\y=\frac{2}{3}\\y=0\end{cases}}\)
