\(\text{1) }3x^3-48x=0\\ \Leftrightarrow x\left(3x^2-48\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\3x^2-48=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\3x^2=48\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=16\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm4\end{matrix}\right.\\ \text{Vậy }x=0\text{ hoặc }x=\pm4\)
\(\text{2) }x^3+x^2-4x=4\\ \Leftrightarrow x^3+x^2-4x-4=0\\ \Leftrightarrow\left(x^3+x^2\right)-\left(4x+4\right)=0\\ \Leftrightarrow x^2\left(x+1\right)-4\left(x+1\right)=0\\ \Leftrightarrow\left(x^2-4\right)\left(x+1\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+2=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\\x=1\end{matrix}\right.\\ \text{Vậy }x=2\text{ hoặc }x=-2\text{ hoặc }x=1\)
1) \(3x^3-48x=0\)
\(\Leftrightarrow3x\left(x^2-16\right)=0\)
\(\Leftrightarrow3x\left(x^2-4^2\right)=0\)
\(\Leftrightarrow3x\left(x-4\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=0\\x-4=0\\x+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
Vậy x=0 ; x=4 ; x=-4
b) \(x^3+x^2-4x=4\)
\(\Leftrightarrow x^3+x^2-4x-4=0\)
\(\Leftrightarrow\left(x^3+x^2\right)-\left(4x+4\right)=0\)
\(\Leftrightarrow x^2\left(x+1\right)-4\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-4\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-2^2\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-2=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2\\x=-2\end{matrix}\right.\)
Vậy x=-1 ; x=2 ; x=-2
