Đáp án: $x∈\{2,5;1;2;5\}$
Giải thích các bước giải:
$2x^4-21x^3+74x^2-105x+50=0$
$⇔2x^4-5x^3-16x^3+40x^2+34x^2-85x-20x+50=0$
$⇔(2x^4-5x^3)-(16x^3-40x^2)+(34x^2-85x)-(20x-50)=0$
$⇔x^3(2x-5)-8x^2(2x-5)+17x(2x-5)-10(2x-5)=0$
$⇔(2x-5)(x^3-8x^2+17x-10)=0$
$⇔(2x-5)(x^3-2x^2-6x^2+12x+5x-10)=0$
$⇔(2x-5)[(x^3-2x^2)-(6x^2-12x)+(5x-10)]=0$
$⇔(2x-5)[x^2(x-2)-6x(x-2)+5(x-2)]=0$
$⇔(2x-5)(x-2)(x^2-6x+5)=0$
$⇔(2x-5)(x-2)(x^2-x-5x+5)=0$
$⇔(2x-5)(x-2)[(x^2-x)-(5x-5)]=0$
$⇔(2x-5)(x-2)[x(x-1)-5(x-1)]=0$
$⇔(2x-5)(x-2)(x-5)(x-1)=0$
$⇔\left[ \begin{array}{l}2x-5=0\\x-2=0\\x-5=0\\x-1=0\end{array} \right.$
$⇔\left[ \begin{array}{l}x=2,5\\x=2\\x=5\\x=1\end{array} \right.$
