1.Rút gọn: A= \(\left(\frac{1}{\sqrt{x}-\sqrt{x-1}}-\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\right)\left(\frac{2}{\sqrt{2}-\sqrt{x}}-\frac{\sqrt{x}+\sqrt{2}}{\sqrt{2x}-x}\right)\)
2.Giải phương trình
a) \(2\sqrt{x^2-4}-3=6\sqrt{x-2}-\sqrt{x+2}\)
b) \(\left\{{}\begin{matrix}\sqrt{x+3y}+\sqrt{x+y}=2\\\sqrt{x+y}+y-x=1\end{matrix}\right.\)
gấp lắm, ai giúp với
2.
a, ĐKXĐ : \(x\ge2\)
\(\text{Đặt }\left\{{}\begin{matrix}\sqrt{x-2}=a\\\sqrt{x+2}=b\end{matrix}\right.\text{ }\left(a,b\ge0\right)\)
\(pt\Leftrightarrow2ab-3=6a-b\)
\(\Leftrightarrow\left(2ab-6a\right)+\left(b-3\right)=0\)
\(\Leftrightarrow\left(b-3\right)\left(2a+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}b=3\\a=-\frac{1}{2}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+2}=3\\\sqrt{x-2}=-\frac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=9\\\text{vô nghiệm}\end{matrix}\right.\Leftrightarrow x=7\left(TM\right)\)
