Question

Giải phương trình sau:
x³ - 3x² - 3x + 1 = 0

Answer 1

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

\(\Leftrightarrow\left(x+1\right)\left(x^2-4x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x^2-4x+1=0\end{matrix}\right.\)

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

Answer 2

Ta có: \(x^3-3x^2-3x+1=0\)

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

\(\Leftrightarrow\left(x+1\right)\left(x^2-4x+1\right)=0\)

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