a.
\(\sqrt{4x^2-4x+1}-7=0\)
\(\Leftrightarrow\sqrt{\left(x-1\right)^2}=7\)
\(\Leftrightarrow\left|x-1\right|=7\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=7\\x-1=-7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-6\end{matrix}\right.\)
b.
ĐKXĐ: \(x\ge1\)
\(\sqrt{25\left(x-1\right)}-\sqrt{x-1}=6+\dfrac{15}{2}\sqrt{\dfrac{x-1}{9}}\)
\(\Leftrightarrow5\sqrt{x-1}-\sqrt{x-1}=6+\dfrac{15}{2.3}\sqrt{x-1}\)
\(\Leftrightarrow4\sqrt{x-1}=6+\dfrac{5}{2}\sqrt{x-1}\)
\(\Leftrightarrow\dfrac{3}{2}\sqrt{x-1}=6\)
\(\Leftrightarrow\sqrt{x-1}=4\)
\(\Leftrightarrow x-1=16\)
\(\Leftrightarrow x=17\)
\(\sqrt{\left(2x-1\right)^2}=7\)
\(\left|2x-1\right|=7\)
\(\left[{}\begin{matrix}2x-1=7\\2x-1=-7\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=4\\x=-3\end{matrix}\right.\)
a)
\(\sqrt{\left(4x^2-4x+1^2\right)}-7=0\)
\(\sqrt{\left(2x-1\right)^2}-7=0\)
\(\left|2x-1\right|-7=0\)
\(\left|2x-1\right|=7\)
Th1 Th2
\(2x-1=7\) \(2x-1=-7\)
\(2x=8\) \(2x=-6\)
\(x=4\) \(x=-6\)
