Tìm số hữu tỉ x biết (x-1/2)^2=0

a/ \(\left(x-\dfrac{1}{2}\right)^2=0\)

\(\Leftrightarrow x-\dfrac{1}{2}=0\)

\(\Leftrightarrow x=\dfrac{1}{2}\)

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b/ \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{4}\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(x+\dfrac{1}{2}\right)^2=\left(\dfrac{1}{2}\right)^2\\\left(x+\dfrac{1}{2}\right)^2=\left(-\dfrac{1}{2}\right)^2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{1}{2}\\x+\dfrac{1}{2}=-\dfrac{1}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)

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c/ \(\left(2x-3\right)^3=-8\)

\(\Leftrightarrow\left(2x-3\right)^3=\left(-2\right)^3\)

\(\Leftrightarrow2x-3=-2\)

\(\Leftrightarrow x=\dfrac{1}{2}\)

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d/ \(\left(3x-2\right)^5=-243\)

\(\left(3x-2\right)^5=\left(-3\right)^5\)

\(\Leftrightarrow3x-2=-3\)

\(\Leftrightarrow x=-\dfrac{1}{3}\)

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e/ \(\left(x-1\right)^3=-125\)

\(\Leftrightarrow\left(x-1\right)^3=\left(-5\right)^3\)

\(\Leftrightarrow x-1=-5\)

\(\Leftrightarrow x=-4\)

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

\(\Leftrightarrow\left[{}\begin{matrix}\left(2x-1\right)^4=3^4\\\left(2x-1\right)^4=\left(-3\right)^4\end{matrix}\right.\)

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

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

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

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\\left[{}\begin{matrix}2x-1=1\\2x-1=-1\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\\left[{}\begin{matrix}x=1\\x=0\end{matrix}\right.\end{matrix}\right.\)

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