a) \(\left(x-3\right)\left(x+3\right)=\left(x-2\right)^2-1\)
\(\Leftrightarrow x^2-9=x^2-4x+4-1\)
\(\Leftrightarrow4x=12\)
\(\Leftrightarrow x=3\)
b) \(\left(2x-1\right)^2=\left(2x+5\right)\left(2x-5\right)+2\)
\(\Leftrightarrow4x^2-4x+1=4x^2-25+2\)
\(\Leftrightarrow4x=24\)
\(\Leftrightarrow x=6\)
c) \(\left(x+1\right)^3=x^2\left(x-2\right)+5\left(x^2-1\right)\)
\(\Leftrightarrow x^3+3x^2+3x+1=x^3-2x^2+5x^2-5\)
\(\Leftrightarrow3x=-6\)
\(\Leftrightarrow x=-2\)
d) \(\left(x^2-3x+9\right)\left(x+3\right)=\left(x-2\right)^3+\left(3x-1\right)\left(2x+3\right)\)
\(\Leftrightarrow x^3+3^3=x^3-6x^2+12x-8+6x^2+7x-3\)
\(\Leftrightarrow x^3+27=x^3+19x-11\)
\(\Leftrightarrow19x=38\)
\(\Leftrightarrow x=2\)
