Question

2. Tìm x để các biểu thức sau có nghĩa:
a) \(\sqrt{9-x^2}\) b) \(\sqrt{\dfrac{1}{x^2-4}}\)
c) \(\dfrac{1}{\sqrt{x}+2}+\dfrac{\sqrt{x}}{\sqrt{x}-3}\)

 

Answer 1

\(a,ĐKXĐ:9-x^2\ge0\\ \Leftrightarrow x^2\le9\\ \Leftrightarrow-3\le x\le3\\ b,ĐKXĐ:\dfrac{1}{x^2-4}\ge0\\ \Leftrightarrow x^2-4\le0\\ \Leftrightarrow x^2\le4\\ \Leftrightarrow-2\le x\le2\\ c,ĐKXĐ:\left\{{}\begin{matrix}\sqrt{x}+2\ne0\left(luôn.đúng\right)\\x\ge0\end{matrix}\right.\\ \Leftrightarrow x\ge0\\ d,ĐKXĐ:\left\{{}\begin{matrix}x\ge0\\\sqrt{x}-3\ne0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\sqrt{x}\ne3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne9\end{matrix}\right.\)