Giải:
a) \(\sqrt{\left(x-3\right)^2}=3-x\)
\(\Leftrightarrow\left|x-3\right|=3-x\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=3-x\\x-3=x-3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+x=3+3\\x-x=-3+3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=6\\0x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\0x=0\end{matrix}\right.\)
Vậy ...
b) \(\sqrt{25-20x+4x^2}+2x=5\)
\(\Leftrightarrow\sqrt{5^2-2.5.2x+\left(2x\right)^2}+2x=5\)
\(\Leftrightarrow\sqrt{\left(5-2x\right)^2}+2x=5\)
\(\Leftrightarrow\left|5-2x\right|+2x=5\)
\(\Leftrightarrow\left|5-2x\right|=5-2x\)
\(\Leftrightarrow\left[{}\begin{matrix}5-2x=5-2x\\5-2x=2x-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-2x+2x=5-5\\-2x-2x=-5-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}0x=0\\-4x=-10\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}0x=0\\x=\dfrac{5}{2}\end{matrix}\right.\)
Vậy ...
c) \(\sqrt{1-12x+36x^2}=5\)
\(\Leftrightarrow\sqrt{\left(1-6x\right)^2}=5\)
\(\Leftrightarrow\left|1-6x\right|=5\)
\(\Leftrightarrow\left[{}\begin{matrix}1-6x=5\\1-6x=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}6x=1-5\\6x=1-\left(-5\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}6x=-4\\6x=6\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{2}{3}\\x=1\end{matrix}\right.\)
Vậy ...
