Question

Answer 1

d: \(\left(2x-3\right)^2-\left(2x+1\right)^2=24\)

=>\(4x^2-12x+9-4x^2-4x-1=24\)

=>-16x+8=24

=>-16x=16

=>x=-1

e: \(\left(2x-1\right)^2-\left(4x^2-1\right)=0\)

=>\(4x^2-4x+1-4x^2+1=0\)

=>-4x+2=0

=>-4x=-2

=>\(x=\dfrac{1}{2}\)

Answer 2

e) \(\left(2x-1\right)^2-\left(4x^2-1\right)=0\)

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

\(\Leftrightarrow\left(2x-1\right)\left(2x-1-2x-1\right)=0\)

\(\Leftrightarrow-2\left(2x-1\right)=0\)

\(\Leftrightarrow2x-1=0\)

\(\Leftrightarrow x=\dfrac{1}{2}\)