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\(a,\frac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}\)\(ĐKXĐ:x\ge-\frac{5}{7}\)
\(\Leftrightarrow9x-7=7x+5\)
\(\Leftrightarrow9x-7x=5+7\)
\(\Leftrightarrow2x=12\)
\(\Leftrightarrow x=6\)
\(b,\sqrt{4x-20}+3\sqrt{\frac{x-5}{9}}-\frac{1}{3}\sqrt{9x-45}=4\)
\(\Leftrightarrow\sqrt{4\left(x-5\right)}+3.\frac{\sqrt{x-5}}{\sqrt{9}}-\frac{1}{3}\sqrt{9\left(x-5\right)}=4\)
\(\Leftrightarrow2\sqrt{x-5}+\sqrt{x-5}-\sqrt{x-5}=4\)
\(\Leftrightarrow\sqrt{x-5}\left(2+1-1\right)=4\)
\(\Leftrightarrow2\sqrt{x-5}=4\)
\(\Leftrightarrow\sqrt{x-5}=2\)
\(\Leftrightarrow x-5=4\)
\(\Leftrightarrow x=9\)
\(\sqrt{\frac{-6}{1+x}}=5\)
\(\Leftrightarrow\sqrt{\frac{-6}{1+x}}^2=5^2\)
\(\Leftrightarrow\frac{-6}{1+x}=25\)
\(\Leftrightarrow x+1=\frac{-6}{25}\)
\(\Leftrightarrow x=\frac{-6}{25}-1=\frac{-31}{25}\)
\(\sqrt{\left(\sqrt{x}-7\right)\left(\sqrt{x}+7\right)}=2\)
\(\Leftrightarrow\sqrt{x-49}=2\)
\(\Leftrightarrow x-49=4\Leftrightarrow x=53\)
ĐKXĐ: \(\left[{}\begin{matrix}x< -2\\x\ge-\frac{2}{5}\end{matrix}\right.\)
\(\Leftrightarrow\frac{8}{5\left(x+2\right)}-1+\sqrt{\frac{5x+2}{x+2}}-\frac{6}{5}=0\)
\(\Leftrightarrow\frac{-\left(5x+2\right)}{5\left(x+2\right)}+\sqrt{\frac{5x+2}{x+2}}-\frac{6}{5}=0\)
Đặt \(\sqrt{\frac{5x+2}{x+2}}=a\ge0\)
\(-\frac{1}{5}a^2+a-\frac{6}{5}=0\Leftrightarrow a^2-5a+6=0\)
\(\Rightarrow\left[{}\begin{matrix}a=2\\a=3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\frac{5x+2}{x+2}=4\\\frac{5x+2}{x+2}=9\end{matrix}\right.\) \(\Rightarrow...\)