Tìm x biết (2x-1)^4=81

1.

a) \(\left(2x-1\right)^4=81\)

\(\left(2x-1\right)^4=\left(\pm3\right)^4\)

\(\Rightarrow\left[{}\begin{matrix}2x-1=3\\2x-1=-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)

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b) \(\left(x-1\right)^5=-32\)

\(\left(x-1\right)^5=\left(-2\right)^5\)

\(\Rightarrow x-1=-2\Rightarrow x=-3\)

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c) \(\left(2x-1\right)^6=\left(2x-1\right)^8\)

\(\Leftrightarrow\left(2x-1\right)^6-\left(2x-1\right)^8=0\)

\(\Leftrightarrow\left(2x-1\right)^6\left[1-\left(2x-1\right)^2\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(2x-1\right)^6=0\\1-\left(2x-1\right)^2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x-1=0\\\left(2x-1\right)^2=1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\\left(2x-1\right)^2=\left(\pm1\right)^2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\\left[{}\begin{matrix}2x-1=1\\2x-1=-1\end{matrix}\right.\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\\x=x=0\end{matrix}\right.\)

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