Bài 1: tìm x không âm biết:
a, \(\sqrt{x-1}\) \(\ge\) 4
b, \(\sqrt{1-x\le2}\)
Bài 2: tìm x để các căn thức sau xác định:
a, \(\sqrt{1-2x}\) b, \(\sqrt{x+5}\) c, \(\sqrt{3-4x}\)
d,\(\sqrt{\dfrac{4}{1+x}}\) e, \(\sqrt{\dfrac{-4}{1-x}}\) g, \(\sqrt{\left(x+2\right)\left(x-5\right)}\)
h, \(\sqrt{\dfrac{x+1}{x-3}}\)
câu h (bao hàm hết)
\(H=\sqrt{\dfrac{x+1}{x-3}}\)
\(\dfrac{x+1}{x-3}\ge0\Leftrightarrow\left\{{}\begin{matrix}x\ne3\\\left(x+1\right)\left(x-3\right)\ge0\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x\ne3\\\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1\ge0\\x-3\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1\le0\\x-3\le0\end{matrix}\right.\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne3\\\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge-1\\x\ge3\end{matrix}\right.\\\left\{{}\begin{matrix}x\le-1\\x\le3\end{matrix}\right.\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne3\\\left[{}\begin{matrix}x\ge3\\x\le-1\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x>3\\x\le-1\end{matrix}\right.\)