a: \(x^2-4x+4=25\)
=>\(\left(x-2\right)^2=25\)
=>\(\left[{}\begin{matrix}x-2=5\\x-2=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-3\end{matrix}\right.\)
b: \(\dfrac{x-17}{1990}+\dfrac{x-21}{1986}+\dfrac{x+1}{1004}=4\)
=>\(\left(\dfrac{x-17}{1990}-1\right)+\left(\dfrac{x-21}{1986}-1\right)+\left(\dfrac{x+1}{1004}-2\right)=0\)
=>\(\dfrac{x-2007}{1990}+\dfrac{x-2007}{1986}+\dfrac{x-2007}{1004}=0\)
=>x-2007=0
=>x=2007
c: \(4^x-12\cdot2^x+32=0\)
=>\(\left(2^x\right)^2-4\cdot2^x-8\cdot2^x+32=0\)
=>\(\left(2^x-4\right)\left(2^x-8\right)=0\)
=>\(\left[{}\begin{matrix}2^x-4=0\\2^x-8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
