Question

giải phương trình sau:

\(\sqrt{\left(x-3\right)^2}=3-x\)

Answer 1

\(\sqrt{\left(x-3\right)^2}=3-x\)

⇔ \(\left|x-3\right|=3-x\)

⇔ \(\left\{{}\begin{matrix}x-3\ge0\\\left[{}\begin{matrix}x-3=3-x\\x-3=x-3\end{matrix}\right.\end{matrix}\right.\)

⇔\(\left\{{}\begin{matrix}x\ge3\\\left[{}\begin{matrix}x+x=3+3\\x-x=-3+3\end{matrix}\right.\end{matrix}\right.\)

⇔\(\left\{{}\begin{matrix}x\ge3\\\left[{}\begin{matrix}2\text{x = 6}\\0\text{x}=0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x\ge3\\\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\end{matrix}\right.\left(nh\text{ận}\right)\)

⇔ \(x=3\)

Vậy S= \(\left\{3\right\}\)