a/ \(x^2-4x+1=\left(x-2+\sqrt{3}\right)\left(x-2-\sqrt{3}\right)\)
Để biểu thức có nghĩa
\(\Leftrightarrow\left(x-2+\sqrt{3}\right)\left(x-2-\sqrt{3}\right)\ge0\)
\(\Leftrightarrow\left[{}\begin{matrix}x\ge2+\sqrt{3}\\x\le2-\sqrt{3}\end{matrix}\right.\)
b/ Để biểu thức có nghĩa
\(\Leftrightarrow\left\{{}\begin{matrix}\frac{2x-1}{x+3}\ge0\\x+3\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-1\ge0\\x+3\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-1\le0\\x+3\le0\end{matrix}\right.\end{matrix}\right.\\x\ne-3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x\ge\frac{1}{2}\\x\le-3\end{matrix}\right.\\x\ne-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\ge\frac{1}{2}\\x< -3\end{matrix}\right.\)