\(x^3-7x-6=0\)
\(\Leftrightarrow x^3-x-6x-6=0\)
\(\Leftrightarrow x\left(x^2-1\right)-6\left(x+1\right)=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left[x\left(x-1\right)-6\right]=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x^2-x-6=0\left(2\right)\end{matrix}\right.\)
\(\left(2\right)\Leftrightarrow x^2-3x+2x-6=0\)
\(\Leftrightarrow x\left(x-3\right)+2\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
Vậy \(S=\left\{-1;-2;3\right\}\)
\(x^3-x-6x+6=0\)
\(\left(x^3-x\right)-\left(6x-6\right)=0\)
\(x\left(x^2-1\right)-6\left(x-1\right)=0\)
\(\left(x-1\right)\left(x\left(x+1\right)-6\right)=0\)
\(\left(x-1\right)\left(x^2+x-6\right)=0\)
\(\left(x-1\right)\left(x^2-3x+2x-6\right)=0\)
\(\left(x-1\right)\left(x-3\right)\left(x+2\right)=0\)
\(\left[{}\begin{matrix}x=1\\x=3\\x=-2\end{matrix}\right.\)
x3 - 7x - 6 = 0
<=> x3 - x - 6x - 6 = 0
<=> x ( x - 1) ( x + 1) - 6 (x + 1) = 0
<=> (x + 1) ( x2 - x - 6) = 0
<=> (x + 1) ( x - 3) (x + 2) = 0
vậy x = [ -1 , 3 - 2]
