4: ĐKXĐ: \(x\in R\)
\(\sqrt{x^2-14x+49}=18\)
=>\(\sqrt{\left(x-7\right)^2}=18\)
=>|x-7|=18
=>\(\left[{}\begin{matrix}x-7=18\\x-7=-18\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=25\\x=-11\end{matrix}\right.\)
5: ĐKXĐ: \(x\in R\)
\(\sqrt{4x^2+4x+1}=5\)
=>\(\sqrt{\left(2x+1\right)^2}=5\)
=>|2x+1|=5
=>\(\left[{}\begin{matrix}2x+1=5\\2x+1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=4\\2x=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)
6: ĐKXĐ: \(x\in R\)
\(\sqrt{36x^2-12x+1}=5\)
=>\(\sqrt{\left(6x-1\right)^2}=5\)
=>|6x-1|=5
=>\(\left[{}\begin{matrix}6x-1=5\\6x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}6x=6\\6x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{2}{3}\end{matrix}\right.\)
7: ĐKXĐ: \(x\in R\)
\(\sqrt{16x^2-40x+25}=5\)
=>\(\sqrt{\left(4x-5\right)^2}=5\)
=>|4x-5|=5
=>\(\left[{}\begin{matrix}4x-5=5\\4x-5=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=10\\4x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=0\end{matrix}\right.\)
8: ĐKXĐ: \(x\in R\)
\(\sqrt{4x^2-4x+1}=3\)
=>\(\sqrt{\left(2x-1\right)^2}=3\)
=>|2x-1|=3
=>\(\left[{}\begin{matrix}2x-1=3\\2x-1=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=4\\2x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
9: ĐKXĐ: \(x\in R\)
\(\sqrt{4x^2+12x+9}=3\)
=>\(\sqrt{\left(2x+3\right)^2}=3\)
=>|2x+3|=3
=>\(\left[{}\begin{matrix}2x+3=3\\2x+3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=0\\2x=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\end{matrix}\right.\)
