Question

Tìm x:
x⁴ + 2x³ - 4x - 4 = 0

Answer 1

`(x^2-2)(x^2 + 2x + 2)`

`= (x-sqrt2)(x+sqrt2)(x^2+2x+2)`

Answer 2

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

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

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

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

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

mà \(\left(x+1\right)^2\ge0\)

\(\Rightarrow\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\end{matrix}\right.\)