Question

Answer 1

a: \(4x^2-4=0\)

=>\(x^2-1=0\)

=>\(x^2=1\)

=>\(\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)

c: \(\left(x+3\right)^2-x^2=45\)

=>\(x^2+6x+9-x^2=45\)

=>6x+9=45

=>6x=45-9=36

=>\(x=\dfrac{36}{6}=6\)

d: \(16\left(x-1\right)^2-25=0\)

=>\(\left(4x-4\right)^2-25=0\)

=>\(\left(4x-4-5\right)\left(4x-4+5\right)=0\)

=>(4x-9)(4x+1)=0

=>\(\left[{}\begin{matrix}4x-9=0\\4x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{4}\\x=-\dfrac{1}{4}\end{matrix}\right.\)

e: \(\left(5x-4\right)^2-49x^2=0\)

=>(5x-4-7x)(5x-4+7x)=0

=>(-2x-4)(12x-4)=0

=>\(\left[{}\begin{matrix}-2x-4=0\\12x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{1}{3}\end{matrix}\right.\)

f: 

\(\left(3x-5\right)^2-\left(x+1\right)^2=0\)

=>\(\left(3x-5-x-1\right)\left(3x-5+x+1\right)=0\)

=>(2x-6)(4x-4)=0

=>\(\left[{}\begin{matrix}2x-6=0\\4x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)