Question

\(x^4-4x^3-2x^2+12x+5=0\)

Answer 1

Lời giải:

Ta có:

\(x^4-4x^3-2x^2+12x+5=0\)

\(\Leftrightarrow (x^4-4x^3+4x^2)-6x^2+12x+5=0\)

\(\Leftrightarrow (x^2-2x)^2-6(x^2-2x)+5=0\)

Đặt $x^2-2x=a$. Khi đó:
\(a^2-6a+5=0\)

\(\Leftrightarrow (a-1)(a-5)=0\Rightarrow \left[\begin{matrix} a=1\\ a=5\end{matrix}\right.\)

Nếu $a=1$ thì $x^2-2x=1$

\(\Leftrightarrow x^2-2x-1=0\Rightarrow x=1\pm \sqrt{2}\)

Nếu $a=5$ thì $x^2-2x=5$

\(\Leftrightarrow x^2-2x-5=0\Rightarrow x=1\pm \sqrt{6}\)