1) \(x^3-x^2=4x^2-8x+4\Leftrightarrow x^3-x^2-4x^2+8x-4=0\)
\(\Leftrightarrow x^3-4x^2+4x-x^2+4x-4=0\)
\(x\left(x^2-4x+4\right)-\left(x^2-4x+4\right)=0\Leftrightarrow\left(x-1\right)\left(x^2-4x+4\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)^2=0\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\\x-2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=2\end{matrix}\right.\) vậy \(x=1;x=2\)
2) \(9x^2-49=0\Leftrightarrow\left(3x\right)^2-7^2=0\Leftrightarrow\left(3x-7\right)\left(3x+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-7=0\\3x+7=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}3x=7\\3x=-7\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=\dfrac{-7}{3}\end{matrix}\right.\) vậy \(x=\dfrac{7}{3};x=\dfrac{-7}{3}\) 3) \(x^2-9=5\left(x-3\right)^2\Leftrightarrow x^2-9=5\left(x^2-6x+9\right)\)
\(5x^2-30x+45=x^2-9\Leftrightarrow5x^2-30x+45-x^2+9=0\)
\(\Leftrightarrow4x^2-30x+54=0\Leftrightarrow4x^2-12x-18x+54=0\)
\(\Leftrightarrow4x\left(x-3\right)-18\left(x-3\right)=0\Leftrightarrow\left(4x-18\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}4x-18=0\\x-3=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}4x=18\\x=3\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{18}{4}=\dfrac{9}{2}\\x=3\end{matrix}\right.\) vậy \(x=\dfrac{9}{2};x=3\)
