b) \(\left(5x+1\right)^2=\left(2x-3\right)^2\)
\(\Leftrightarrow\left(5x+1\right)^2-\left(2x-3\right)^2=0\)
\(\Leftrightarrow\left(5x+1-2x+3\right).\left(5x+1+2x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+4=0\\7x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=-4\\7x=2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\frac{4}{3}\\x=\frac{2}{7}\end{matrix}\right.\)
a) x2 - 9 - 2(x+3)2 = 0
⇔ \(x^2-9-2\left(x^2+6x+9\right)=0\)
⇔ \(x^2-9-2x^2-12x-18=0\)
\(\Leftrightarrow-x^2-12x^{ }-27=0\)
⇔ \(x^2+12x+27=0\)
⇔ \(x^2+9x+3x+27=0\)
⇔ x( x + 9 ) + 3 ( x + 9 ) =0
\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\x+9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-9\end{matrix}\right.\)
