\(a,\sqrt{1-4x+4x^2}=5\left(x\in R\right)\\ \Leftrightarrow\left|2x-1\right|=5\\ \Leftrightarrow\left[{}\begin{matrix}2x-1=5\left(x\ge\dfrac{1}{2}\right)\\2x-1=-5\left(x< \dfrac{1}{2}\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\left(x\ge\dfrac{1}{2}\right)\left(tm\right)\\x=-2\left(x< \dfrac{1}{2}\right)\left(tm\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
\(b,\sqrt{\left(2x-1\right)^2}=3\left(x\in R\right)\\ \Leftrightarrow\left|2x-1\right|=3\\ \Leftrightarrow\left[{}\begin{matrix}2x-1=3\left(x\ge\dfrac{1}{2}\right)\\2x-1=-3\left(x< \dfrac{1}{2}\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(x\ge\dfrac{1}{2}\right)\left(tm\right)\\x=-1\left(x< \dfrac{1}{2}\right)\left(tm\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
\(c,\sqrt{4-5x}=12\left(x\le\dfrac{4}{5}\right)\\ \Leftrightarrow4-5x=144\Leftrightarrow x=-28\left(tm\right)\)
