Question

giải phương trình bâc cao sau:

a, x^3-7x^2+12x-6=0

Answer 1

\(x^3-7x^2+12x-6=0\)

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

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

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

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

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