Question

giải phương trình sau: X⁴ - 4X³ + 3X² + 4X -4 =0

Answer 1

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

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

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

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

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

\(\Leftrightarrow\)  \(^{\left(x-2\right)^2=0}_{x^2-1=0}\)  \(\Leftrightarrow\)  \(^{x-2=0}_{x^2=1}\)  \(\Leftrightarrow\)  \(^{x=2}_{x=^+_-1}\)

Vậy,   \(S=\left\{-1;1;2\right\}\)