a: \(\left(2x-1\right)^2=x^2\)
=>\(\left(2x-1\right)^2-x^2=0\)
=>(2x-1-x)(2x-1+x)=0
=>(x-1)(3x-1)=0
=>\(\left[\begin{array}{l}x-1=0\\ 3x-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=1\\ x=\frac13\end{array}\right.\)
b: \(\left(2x+7\right)^2=9\left(x+2\right)^2\)
=>\(\left(3x+6\right)^2=\left(2x+7\right)^2\)
=>\(\left(3x+6\right)^2-\left(2x+7\right)^2=0\)
=>(3x+6+2x+7)(3x+6-2x-7)=0
=>(5x+13)(x-1)=0
=>\(\left[\begin{array}{l}5x+13=0\\ x-1=0\end{array}\right.\Longrightarrow\left[\begin{array}{l}x=-\frac{13}{5}\\ x=1\end{array}\right.\)
c: \(4\left(2x+7\right)^2-9\left(x+3\right)^2=0\)
=>\(\left(4x+14\right)^2-\left(3x+9\right)^2=0\)
=>(4x+14-3x-9)(4x+14+3x+9)=0
=>(x+5)(7x+23)=0
=>\(\left[\begin{array}{l}x+5=0\\ 7x+23=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-5\\ x=-\frac{23}{7}\end{array}\right.\)
