\(x^3-x-6=0\left(Chữa\text{ }đề\right)\\ \Leftrightarrow x^3-4x-3x-6=0\\ \Leftrightarrow\left(x^3-4x\right)-\left(3x+6\right)=0\\ \Leftrightarrow x\left(x^2-4\right)-3\left(x+2\right)=0\\ \Leftrightarrow x\left(x-2\right)\left(x+2\right)-3\left(x+2\right)=0\\ \Leftrightarrow\left(x^2-2x\right)\left(x+2\right)-3\left(x+2\right)=0\\ \Leftrightarrow\left(x^2-2x-3\right)\left(x+2\right)=0\\ \Leftrightarrow\left(x^2-3x+x-3\right)\left(x+2\right)=0\\ \Leftrightarrow\left[\left(x^2-3x\right)+\left(x-3\right)\right]\left(x+2\right)=0\\ \Leftrightarrow\left[x\left(x-3\right)+\left(x-3\right)\right]\left(x+2\right)=0\\ \Leftrightarrow\left(x+1\right)\left(x-3\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-3=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=3\\x=-2\end{matrix}\right.\\ Vậy\text{ }x=-1\text{ }hoặc\text{ }x=3\text{ }hoặc\text{ }x=-2\)
\(x^3-x+6=0\)
\(\Leftrightarrow x^3-4x-3x+6=0\)
\(\Leftrightarrow\left(x^3-4x\right)-\left(3x-6\right)=0\)
\(\Leftrightarrow x\left(x^2-4\right)-3\left(x-2\right)=0\)
\(\Leftrightarrow x\left(x^2-2^2\right)-3\left(x-2\right)=0\)
\(\Leftrightarrow x\left(x-2\right)\left(x+2\right)-3\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left[x\left(x+2\right)-3\right]\)
\(\Leftrightarrow\left(x-2\right)\left(x^2+2x-3\right)\)
\(\Leftrightarrow\left(x-2\right)\left(x^2-x+3x-3\right)\)
\(\Leftrightarrow\left(x-2\right)\left[\left(x^2-x\right)+\left(3x-3\right)\right]\)
\(\Leftrightarrow\left(x-2\right)\left[x\left(x-1\right)+3\left(x-1\right)\right]\)
\(\Leftrightarrow\left(x-2\right)\left(x-1\right)\left(x+3\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-1=0\\x+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=1\\x=-3\end{matrix}\right.\)
Vậy \(x=2\) ; \(x=1\) ; \(x=-3\)
\(x^3-x+6=0\)
\(\Leftrightarrow x^3-4x+3x+6=0\)
\(\Leftrightarrow\left(x^3-4x\right)+\left(3x+6\right)=0\)
\(\Leftrightarrow x\left(x^2-4\right)+3\left(x+2\right)=0\)
\(\Leftrightarrow x\left(x^2-2^2\right)+3\left(x+2\right)=0\)
\(\Leftrightarrow x\left(x-2\right)\left(x+2\right)+3\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left[x\left(x-2\right)+3\right]=0\)
\(\Leftrightarrow\left(x+2\right)\left(x^2-2x+3\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x^2-2x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x^2-2x+3=0\left(loai\right)\end{matrix}\right.\)
\(\Leftrightarrow x+2=0\)
\(\Leftrightarrow x=-2\)
Vậy x=-2
