a) \(\sqrt{x-1}=3\left(đk:x\ge1\right)\)
\(\Leftrightarrow x-1=9\Leftrightarrow x=10\)
b) \(3\sqrt{4x-12}-5\sqrt{9x-12}=\sqrt{x-3}-20\left(đk:x\ge3\right)\)
\(\Leftrightarrow6\sqrt{x-3}-15\sqrt{x-3}-\sqrt{x-3}=-20\)
\(\Leftrightarrow-10\sqrt{x-3}=-20\)
\(\Leftrightarrow\sqrt{x-3}=2\)
\(\Leftrightarrow x-3=4\Leftrightarrow x=7\left(tm\right)\)
a. \(\sqrt{x-1}=3\left(ĐK:x\ge1\right)\)
<=> \(\left(\sqrt{x-1}\right)^2=3^2\)
<=> \(\left|x-1\right|=9\)
<=> \(\left[{}\begin{matrix}x-1=9\\x-1=-9\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=10\\x=-8\left(loại\right)\end{matrix}\right.\)
b. \(3\sqrt{4x-12}-5\sqrt{9x-27}=\sqrt{x-3}-20\left(ĐK:x\ge3\right)\)
<=> \(3\sqrt{4\left(x-3\right)}-5\sqrt{9\left(x-3\right)}-\sqrt{x-3}+20=0\)
<=> \(3\sqrt{2^2\left(x-3\right)}-5\sqrt{3^2\left(x-3\right)}-\sqrt{x-3}+20=0\)
<=> \(6\sqrt{x-3}-15\sqrt{x-3}-\sqrt{x-3}+20=0\)
<=> \(\left(6-15-1\right)\sqrt{x-3}=-20\)
<=> \(-10\sqrt{x-3}=-20\)
<=> \(\sqrt{x-3}=2\)
<=> \(\left(\sqrt{x-3}\right)^2=2^2\)
<=> \(\left|x-3\right|=4\)
<=> \(\left[{}\begin{matrix}x-3=4\\x-3=-4\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=7\\x=-1\left(loại\right)\end{matrix}\right.\)
