Question

tìm x để căn (x+1)(x-3) có nghĩa

Answer 1

\(\sqrt{\left(x+1\right)\left(x-3\right)}\) có nghĩa khi:

\(\left(x+1\right)\left(x-3\right)\ge0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1\ge0\\x-3\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1\le0\\x-3\le0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge-1\\x\ge3\end{matrix}\right.\\\left\{{}\begin{matrix}x\le-1\\x\le3\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x\ge3\\x\le-1\end{matrix}\right.\)

Vậy \(\sqrt{\left(x+1\right)\left(x-3\right)}\) xác định khi: \(\left[{}\begin{matrix}x\le-1\\x\ge3\end{matrix}\right.\)