Question

giải phương trình : x³ -2x²-5x +6=0

Answer 1

\(x^3-2x^2-5x+6=0\)

\(\Leftrightarrow x^2\left(x-1\right)-x\left(x-1\right)-6\left(x-1\right)=0\)

\(\Leftrightarrow\left(x^2-x-6\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x+2\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+2=0\\x-1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\\x=1\end{matrix}\right.\)

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Answer 2

\(x^3-2x^2-5x+6=0\\ \Leftrightarrow x^3-3x^2+x^2-3x-2x+6=0\\ \Leftrightarrow x^2\left(x-3\right)+x\left(x-3\right)-2\left(x-3\right)=0\\ \Leftrightarrow\left(x-3\right)\left(x^2-x-2\right)=0\\ \Leftrightarrow\left(x-3\right)\left(x+2\right)\left(x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+2=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\\x=1\end{matrix}\right.\)

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