Ta có: \(\left(4x-1\right)^{30}=\left(4x-1\right)^{20}\)
\(\Rightarrow\left(4x-1\right)^{30}-\left(4x-1\right)^{20}=0\)
\(\Rightarrow\left(4x-1\right)^{20}.\left[\left(4x-1\right)^{10}-1\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(4x-1\right)^{20}=0\\\left[\left(4x-1\right)^{10}-1\right]=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}4x-1=0\\\left(4x-1\right)^{10}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=1\\4x-1=1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{4}\\4x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{4}\\x=\frac{2}{4}=\frac{1}{2}\end{matrix}\right.\)
Vậy: \(x\in\left\{\frac{1}{2};\frac{1}{4}\right\}\)
\(\left(4x-1\right)^{30}=\left(4x-1\right)^{20}\)
\(\Rightarrow\left(4x-1\right)^{30}-\left(4x-1\right)^{20}=0\)
\(\Rightarrow\left(4x-1\right)^{20}.\left[\left(4x-1\right)^{10}-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(4x-1\right)^{20}=0\\\left(4x-1\right)^{10}-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}4x-1=0\\\left(4x-1\right)^{10}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}4x=1\\4x-1=1\\4x-1=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{1}{4}\\4x=2\\4x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{1}{4}\\x=\frac{1}{2}\\x=0\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{1}{4};\frac{1}{2};0\right\}.\)
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