Question

Giải pt

\(x^3-7x^2=3x^2-12x\)

Answer 1

\(x^3-7x^2=3x^2-12x\)

\(\Leftrightarrow x^3-10x^2+12x=0\Leftrightarrow x\left(x^2-10x+12\right)=0\)

\(\Leftrightarrow x\left(x-5-\sqrt{13}\right)\left(x-5+\sqrt{13}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=5+\sqrt{13}\\x=5-\sqrt{13}\end{matrix}\right.\)

Answer 2

<=>\(x^3-10x^2+12x=0\)

<=>\(x\left(x^2-10x+12\right)=0\)

<=>\(x\left(x-5-\sqrt{13}\right)\left(x-5+\sqrt{13}\right)=0\)

<=>\(\left[{}\begin{matrix}x=0\\x-5-\sqrt{13}=0\\x-5+\sqrt{13}=0\end{matrix}\right.\)

<=>\(\left[{}\begin{matrix}x=0\\x=5+\sqrt{13}\\x=5-\sqrt{13}\end{matrix}\right.\)