\(5\sqrt{x-1}-\sqrt{x+7}=3x-4\)
ĐK: \(\left\{{}\begin{matrix}x-1\ge0\\x+7\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\x\ge-7\end{matrix}\right.\Leftrightarrow x\ge1\)
\(pt\Leftrightarrow5\sqrt{x-1}=3x-4+\sqrt{x+7}\\ \Leftrightarrow25\left(x-1\right)=\left(3x-4\right)^2+2\left(3x-4\right)\sqrt{x+7}+x+7\\ \Leftrightarrow25x-25=9x^2-24x+16+\left(6x-8\right)\sqrt{x+7}+x+7\\ \Leftrightarrow9x^2-24x-25x+x+16+7+25=-\left(6x-8\right)\sqrt{x+7}\)
\(\Leftrightarrow9x^2-48x+48=\left(8-6x\right)\sqrt{x+7}\\ \Leftrightarrow\left(3x-8\right)^2-16=\left(8-6x\right)\sqrt{x+7}\\ \Leftrightarrow\left(3x-12\right)\left(3x-4\right)=-2\left(3x-4\right)\sqrt{x+7}\)
\(\Leftrightarrow3x-12=-2\sqrt{x+7}\\ \Leftrightarrow\left(3x-12\right)^2=4\left(x+7\right)\\ \Leftrightarrow9x^2-72x+144-4x-28=0\Leftrightarrow9x^2-76x+116=0\)
\(\Delta=\left(-76\right)^2-4.9.116=1600\)
\(\Rightarrow\left\{{}\begin{matrix}x_1=\frac{76+\sqrt{1600}}{2.9}=\frac{58}{9}\left(TM\right)\\x_2=\frac{76-\sqrt{1600}}{2.9}=2\left(TM\right)\end{matrix}\right.\)
