\(1)4x^2+7x=0\\ \Leftrightarrow x\left(4x+7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\4x+7=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{7}{4}\end{matrix}\right.\\ 2)48x-64x^4=0\\ \Leftrightarrow16x\left(3-4x^3\right)\\ \Leftrightarrow\left[{}\begin{matrix}16x=0\\3-4x^3=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x^3=\dfrac{3}{4}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=\sqrt[3]{\dfrac{4}{3}}\end{matrix}\right.\\ 3)\left(x-1\right)^3-x\left(x-2\right)^2=-1\\ \Leftrightarrow\left(x^3-3x^2+3x-1\right)-x\left(x^2-4x+4\right)=-1\\ \Leftrightarrow x^3-3x^2+3x-1-x^3+4x^2-4x=-1\\ \Leftrightarrow x^2-x-1=-1\\ \Leftrightarrow x^2-x=0\\ \Leftrightarrow x\left(x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
\(4x^2+7x=0\)
\(\Leftrightarrow x\left(4x+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{7}{4}\end{matrix}\right.\)
\(48x-6x^4=0\)
\(\Leftrightarrow6x\left(x^3-8\right)=0\)
\(\Leftrightarrow6x\left(x-2\right)\left(x^2+2x+4\right)=0\)
Vì \(x^2+2x+4=\left(x+1\right)^2+3>0\)
\(\Rightarrow6x\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
\(\left(x-1\right)^3-x\left(x-2\right)^2=-1\)
\(\Leftrightarrow x^3-3x^2+3x-1-x^3+4x^2-4x+1=0\)
\(\Leftrightarrow x^2-x=0\)
\(\Leftrightarrow x\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
