a: \(\sqrt{x^2+4x+4}=12\)
=>\(\sqrt{\left(x+2\right)^2}=12\)
=>|x+2|=12
=>\(\left[\begin{array}{l}x+2=12\\ x+2=-12\end{array}\right.\Rightarrow\left[\begin{array}{l}x=10\\ x=-14\end{array}\right.\)
b: \(\sqrt{4x^2-4x+1}=5\)
=>\(\sqrt{\left(2x-1\right)^2}=5\)
=>|2x-1|=5
=>\(\left[\begin{array}{l}2x-1=5\\ 2x-1=-5\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=6\\ 2x=-4\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3\\ x=-2\end{array}\right.\)
c: ĐKXĐ: x>=0
\(\sqrt{x+2\sqrt{x}+1}=3\)
=>\(\sqrt{\left(\sqrt{x}+1\right)^2}=3\)
=>\(\left|\sqrt{x}+1\right|=3\)
=>\(\sqrt{x}+1=3\)
=>\(\sqrt{x}=2\)
=>x=4(nhận)
d: ĐKXĐ: x>=4
\(\sqrt{x+2\sqrt{x-4}-3}=1\)
=>\(\sqrt{x-4+2\sqrt{x-4}+1}=1\)
=>\(\sqrt{\left(\sqrt{x-4}+1\right)^2}=1\)
=>\(\left|\sqrt{x-4}+1\right|=1\)
=>\(\sqrt{x-4}+1=1\)
=>\(\sqrt{x-4}=0\)
=>x-4=0
=>x=4(nhận)
