Đáp án:
\(\left[ \begin{array}{l}x=2\\x=-4\end{array} \right.\)
Giải thích các bước giải:
$x^4+x^3-9x^2+10x-8=0$
$⇔x^4+2x^3-8x^2-x^3-2x^2+8x+x^2+2x-8=0$
$⇔(x^4+2x^3-8x^2)-(x^3+2x^2-8x)+(x^2+2x-8)=0$
$⇔x^2.(x^2+2x-8)-x.(x^2+2x-8)+(x^2+2x-8)=0$
$⇔(x^2+2x-8).(x^2-x+1)=0$
$⇔[ (x^2+4x)-(2x+8)].[(x^2-2\dfrac{1}{2}x+\dfrac{1}{4})+\dfrac{3}{4}]=0$
$⇔[ x.(x+4)-2.(x+4)].[(x+\dfrac{1}{2})^2+\dfrac{3}{4}]=0$
$⇔(x+4).(x-2).[(x+\dfrac{1}{2})^2+\dfrac{3}{4}]=0$
$⇔\left[ \begin{array}{l}x-2=0\\x+4=0\\(x+\dfrac{1}{2})^2+\dfrac{3}{4}=0\end{array} \right.$
$⇔\left[ \begin{array}{l}x=2\\x=-4\\(x+\dfrac{1}{2})^2+\dfrac{3}{4}=0(vô lí)\end{array} \right.$
