Question

Tìm x để các căn thức sau có nghĩa:

1) \(\sqrt{-3x+1}\)

2)\(\sqrt{2x+3}\)

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

4)\(\sqrt{\frac{3}{5x-1}}\)

5)\(\sqrt{\left(x+2\right)\left(x-5\right)}\)

Answer 1

\(\sqrt{2x+3}\) có nghĩa khi 

\(2x+3\ge0\)

\(\Leftrightarrow2x\ge-3\)

\(\Leftrightarrow x\ge-\frac{3}{2}\)

Vậy .....

Answer 2

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 \(\Leftrightarrow\sqrt{\frac{-1}{2x+1}}\ge0\Leftrightarrow\frac{-1}{2x+1}\ge0\Leftrightarrow2x+1< 0\Leftrightarrow2x< -1\Leftrightarrow x< \frac{-1}{2}\)

Answer 3

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 \(x\le-2\)