Question

a,(2x-5)^2-x^2=0

b.(x^2-2x+1)-9x^2=0

Answer 1

a) \(\left(2x-5\right)^2-x^2=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{5}{3}\end{matrix}\right.\)

b) \(\left(x^2-2x+1\right)-9x^2=0\)

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

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

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