Question

Answer 1

\(\sqrt{x^2-6x+9}=2x-1\Leftrightarrow\sqrt{\left(x-3\right)^2}=2x-1\)

\(\Leftrightarrow\left|x-3\right|=2x-1\Rightarrow\left\{{}\begin{matrix}2x-1\ge0\\\left[{}\begin{matrix}x-3=2x-1\\x-3=1-2x\end{matrix}\right.\end{matrix}\right.\)

 \(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{2}\\\left[{}\begin{matrix}x=-2\left(loại\right)\\x=\dfrac{4}{3}\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow x=\dfrac{4}{3}\)