Question

Tìm x để biểu thức sau có nghĩa:

a)\(\sqrt{\frac{2x-3}{x}}\)

b)\(\sqrt{x-2}+\sqrt{5-x}\)

c)\(\sqrt{\frac{x-1}{x+2}}\)

Answer 1

a/ \(\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-3\ge0\\x>0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-3\le0\\x< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x\ge\frac{3}{2}\\x< 0\end{matrix}\right.\)

b/ \(\left\{{}\begin{matrix}x-2\ge0\\5-x\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\x\le5\end{matrix}\right.\Leftrightarrow2\le x\le5\)

c/ \(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1\ge0\\x+2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1\le0\\x+2< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\ge1\\x< -2\end{matrix}\right.\)