\(\sqrt{2x+3}\) có nghĩa khi
\(2x+3\ge0\)
\(\Leftrightarrow2x\ge-3\)
\(\Leftrightarrow x\ge-\frac{3}{2}\)
Vậy .....
1) \(\sqrt{-3x+1}\) có nghĩa \(\Leftrightarrow\sqrt{-3x+1}\ge0\)
\(\Leftrightarrow-3x+1\ge0\Leftrightarrow-3x\ge-1\Leftrightarrow x\le\frac{1}{3}\)
2) \(\sqrt{2x+3}\) có nghĩa \(\Leftrightarrow\sqrt{2x+3}\ge0\Leftrightarrow2x+3\ge0\Leftrightarrow2x\ge-3\Leftrightarrow x\ge\frac{-3}{2}\)
3) \(\sqrt{\frac{-1}{2x+1}}\) có nghĩa \(\Leftrightarrow\sqrt{\frac{-1}{2x+1}}\ge0\Leftrightarrow\frac{-1}{2x+1}\ge0\Leftrightarrow2x+1< 0\Leftrightarrow2x< -1\Leftrightarrow x< \frac{-1}{2}\)
4) \(\sqrt{\frac{3}{5x-1}}\) có nghĩa \(\Leftrightarrow\sqrt{\frac{3}{5x-1}}\ge0\Leftrightarrow\frac{3}{5x-1}\ge0\Leftrightarrow5x-1>0\Leftrightarrow5x>1\Leftrightarrow x>\frac{1}{5}\)
5) \(\sqrt{\left(x+2\right)\left(x-5\right)}\) có nghĩa
\(\Leftrightarrow\sqrt{\left(x+2\right)\left(x-5\right)}\ge0\)
\(\Leftrightarrow\left(x+2\right)\left(x-5\right)\ge0\)
\(\Leftrightarrow\hept{\begin{cases}x+2\ge0\\x-5\ge0\end{cases}}\) hoặc \(\hept{\begin{cases}x+2\le0\\x-5\le0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x\ge-2\\x\ge5\end{cases}}\) hoặc \(\hept{\begin{cases}x\le-2\\x\le5\end{cases}}\)
Vậy \(x\ge5\) hoặc \(x\le-2\)