a) \(\sqrt{x^2-9}-3\sqrt{x-3}=0\\ \Leftrightarrow\sqrt{\left(x-3\right)\left(x+3\right)}-3\sqrt{x-3}=0\\ \Leftrightarrow\sqrt{x-3}\left(\sqrt{x+3}-3\right)=0\\ \Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-3}=0\\\sqrt{x+3}=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=3\\x=6\end{matrix}\right.\)
S = (3;6)
b)\(\sqrt{x^2-4}-2\sqrt{x-2}=0\\ \Leftrightarrow\sqrt{x-2}\left(\sqrt{x+2}-2\right)=0\\ \Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-2}=0\\\sqrt{x+2}=2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=2\\x=2\end{matrix}\right.\) S= (2)
c)\(\sqrt{\frac{2x-3}{x-1}}=2\left(đkxđ:x\ne1\right)\Leftrightarrow2\sqrt{x-1}=\sqrt{2x-3}\\ \Leftrightarrow2x=1\Leftrightarrow x=\frac{1}{2}\) S= (1/2)
d) đkxđ : x khác -1
\(\sqrt{\frac{4x+3}{x+1}}=3\Leftrightarrow4x+3=9x+9\Leftrightarrow x=-\frac{6}{5}\) S = (-6/5)
e) đk x >= 3/2
\(\frac{\sqrt{2x-3}}{\sqrt{x-1}}=2\Leftrightarrow2x-3=4x-4\Leftrightarrow x=\frac{1}{2}\) (loại) vậy pt vô nghiệm
f) đk x >= -3/4
\(\frac{\sqrt{4x+3}}{\sqrt{x+1}}=3\Leftrightarrow4x+3=9x+9\Leftrightarrow x=-\frac{6}{5}\) (loại) vậy pt vô nghiệm
