$(3y-1)^{10}=(3y-1)^{20}$
$⇔(3y-1)^{10}-(3y-1)^{20}=0$
$⇔(3y-1)^{10}-(3y-1)^{10}.(3y-1)^{10}=0$
$⇔[(3y-1)^{10}-1].(3y-1)^{10}=0$
$⇔$\(\left[ \begin{array}{l}(3y-1)^{10}-1=0\\(3y-1)^{10}=0\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}(3y-1)^{10}=1\\3y-1=0\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}3y-1=0\\3y-1=1\\3y-1=-1\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}y=\frac{1}{3}\\y=\frac{2}{3}\\y=0\end{array} \right.\)
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