Question

tìm điều kiện xác định

a, \(\sqrt{x^2-4}+2\sqrt{x-2}\)

b, \(\sqrt{\left(3-x\right)\left(x+2\right)}\)

c, \(\sqrt{x^2-6x}\)

Answer 1

c) ĐKXĐ:

\(x^2-6x\ge0\Leftrightarrow x.\left(x-6\right)\ge0\)

\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\x-6\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}x\le0\\x-6\le0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\ge6\\x\le0\end{matrix}\right.\)

Answer 2

a) ĐKXĐ: \(\left\{{}\begin{matrix}x^2-4\ge0\\x-2\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x^2\ge4\\x\ge2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x\ge2\\x\le-2\end{matrix}\right.\)

Answer 3

b) ĐKXĐ:
\(\left(3-x\right).\left(x+2\right)\ge0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3-x\ge0\\x+2\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}3-x\le0\\x+2\le0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-2\le x\le3\\3\le x\le-2\left(loai\right)\end{matrix}\right.\)