a) \(\sqrt{4x-12}+\sqrt{x-3}-\dfrac{1}{3}\sqrt{9x-27}=8\)(*)
Đk: \(x\ge3\)
(*)\(\Rightarrow2\sqrt{x-3}+\sqrt{x-3}-\sqrt{x-3}=8\)
\(\Leftrightarrow\sqrt{x-3}=4\)
\(\Leftrightarrow x=19\)( nhận)
Vậy S=\(\left\{19\right\}\)
b)\(\sqrt{x^2-2x+4}=2x-2\) Đk \(x^2-2x+4=\left(x-1\right)^2+3>0\forall x\in R\)
\(\Leftrightarrow x^2-2x+4=4x^2-8x+4\)
\(\Leftrightarrow3x^2-6x=0\)
\(\Leftrightarrow3x\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=2\left(nhận\right)\end{matrix}\right.\)
Vậy S=\(\left\{2\right\}\)
c)\(\sqrt{x^2-10x+25}-5=3x\) ĐK \(x^2-10x+25=\left(x-5\right)^2>0\forall x\in R\)
\(\Leftrightarrow\sqrt{\left(x-5\right)^2}=3x-5\)
\(\Leftrightarrow\left|x-5\right|=3x-5\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=3x-5\\x-5=5-3x\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=\dfrac{10}{4}=\dfrac{5}{2}\left(nhận\right)\end{matrix}\right.\)
Vậy S=\(\left\{\dfrac{5}{2}\right\}\)
