Question

Giải phương trình
x⁴ - 3x³ - 2x² + 6x + 4 = 0

Answer 1

\(x^4-3x^3-2x^2+6x+4=0\)

\(\Leftrightarrow x^4-2x^3-2x^2-x^3+2x^2+2x-2x^2+4x+4=0\)

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

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

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

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