\(\left(2x-1\right)^{10}=\left(2x-1\right)^{100}\)
\(\Rightarrow\left(2x-1\right)^{100}-\left(2x-1\right)^{10}=0\)
\(\Rightarrow\left(2x-1\right)^{10}.\left[\left(2x-1\right)^{90}-1\right]=0\)
\(\Rightarrow\left(2x-1\right)^{10}=0\) hoặc \(\left(2x-1\right)^{90}-1=0\)
\(\Rightarrow2x=1\) hoặc \(\left(2x-1\right)^{90}-1=1\)
\(\Rightarrow x=\dfrac{1}{2}\) hoặc \(2x-1=\left\{{}\begin{matrix}1\\-1\end{matrix}\right.\)
\(\Rightarrow x=\dfrac{1}{2}\) hoặc \(x=\left\{{}\begin{matrix}1\\0\end{matrix}\right.\)
(2x - 1)10 = (2x - 1)100
=> (2x -1)10 - (2x - 1)100 = 0
=> (2x - 1)10.[(2x - 1)90 - 1] = 0
=> (2x - 1)10 = 0 hoặc (2x - 1)90 - 1 = 0
=> \(\left[{}\begin{matrix}2x=1\\\left(2x-1\right)^{90}-1=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\2x-1=\left[{}\begin{matrix}1\\-1\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\left[{}\begin{matrix}1\\0\end{matrix}\right.\end{matrix}\right.\)
@Sarutobi Hùng
\(\left(2x-1\right)^{10}=\left(2x-1\right)^{100}\)
\(\Rightarrow\left(2x-1\right)^{10}-\left(2x-1\right)^{100}=0\)
\(\Leftrightarrow\left(2x-1\right)^{10}\left[1-\left(2x-1\right)^{90}\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(2x-1\right)^{10}=0\\1-\left(2x-1\right)^{90}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\\left(2x-1\right)^{90}=1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\\left[{}\begin{matrix}x=1\\x=0\end{matrix}\right.\end{matrix}\right.\)
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