Ta có : \(x^3+8x^2+17x+10=0\)
\(\Leftrightarrow x^3+2x^2+6x^2+12x+5x+10=0\)
\(\Leftrightarrow x^2\left(x+2\right)+6x\left(x+2\right)+5\left(x+2\right)=0\)
\(\Leftrightarrow\left(x^2+6x+5\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+5\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x+5=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-5\\x=-2\end{matrix}\right.\)
Vậy \(x\in\left\{-1,-2,-5\right\}\)
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