a) \(x^3-4x^2-9x+36=0\Leftrightarrow x^3-7x^2+12x+3x^2-21x+36=0\) \(x\left(x^2-7x+12\right)+3\left(x^2-7x+12\right)=0\Leftrightarrow\left(x+3\right)\left(x^2-7x+12\right)=0\) \(\Leftrightarrow\left(x+3\right)\left(x^2-7x+12\right)=0\Leftrightarrow\left(x+3\right)\left(x^2-3x-4x+12\right)=0\) \(\Leftrightarrow\left(x+3\right)\left(x\left(x-3\right)-4\left(x-3\right)\right)=0\Leftrightarrow\left(x+3\right)\left(x-4\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+3=0\\x-4=0\\x-3=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=-3\\x=4\\x=3\end{matrix}\right.\) vậy \(x=-3;x=4;x=3\)
b) \(5x^2-4\left(x^2-2x+1\right)-5=0\) \(\Leftrightarrow5x^2-4x^2+8x-4-5=0\)
\(\Leftrightarrow x^2+8x-9=0\Leftrightarrow x^2-x+9x-9=0\)
\(\Leftrightarrow x\left(x-1\right)+9\left(x-1\right)\Leftrightarrow\left(x+9\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+9=0\\x-1=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=-9\\x=1\end{matrix}\right.\) vậy \(x=-9;x=1\)
c) đề có sai o bn
d) \(x^3-3x+2=0\Leftrightarrow x^3+x^2-2x-x^2-x+2=0\)
\(\Leftrightarrow x\left(x^2+x-2\right)-\left(x^2+x-2\right)=0\Leftrightarrow\left(x-1\right)\left(x^2+x-2\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-x+2x-2\right)=0\Leftrightarrow\left(x-1\right)\left(x\left(x-1\right)+2\left(x-1\right)\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left(x-1\right)=0\) \(\Leftrightarrow\left\{{}\begin{matrix}x-1=0\\x+2=0\\x-1=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=1\\x=-2\\x=1\end{matrix}\right.\)
vậy \(x=1;x=-2\)
