1, \(\left(x+1\right)^2=4\left(x^2-2x+1\right)^2\)

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

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

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

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

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

vậy tập nghiệm của phương trinh \(S=\left\{3;\dfrac{1}{3}\right\}\)

2, \(\left(x^2-9\right)^2-9\left(x-3\right)^2=0\)

\(\Leftrightarrow\left(x^2-9\right)^2-\left(3x-9\right)^2=0\)

\(\Leftrightarrow\left(x^2-9-3x+9\right)\left(x^2-9+3x-9\right)=0\)

\(\Leftrightarrow\left(x^2-3x\right)\left(x^2+3x-18\right)=0\)

\(\Leftrightarrow x\left(x-3\right)\left(x^2+6x-3x-18\right)=0\)

\(\Leftrightarrow x\left(x-3\right)\left(x+6\right)\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-3=0\\x+6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-6\end{matrix}\right.\)

vậy tập nghiệm của phương trinh \(S=\left\{0;3;-6\right\}\)

3, \(9\left(x-3\right)^2=4\left(x+2\right)^2\)

\(\Leftrightarrow\left(3x-9\right)^2-\left(2x+2\right)^2=0\)

\(\Leftrightarrow\left(3x-9-2x-2\right)\left(3x-9+2x+2\right)=0\)

\(\Leftrightarrow\left(x-11\right)\left(5x-7\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-11=0\\5x-7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=11\\x=\dfrac{7}{5}\end{matrix}\right.\)

vậy tập nghiệm của phương trinh \(S=\left\{11;\dfrac{7}{5}\right\}\)