$x^4-3x^2+31x-30=0$
$⇒(x^4-2x^2+1)+(31x-31)=0$
$⇒(x^2-1)^2+31(x-1)=0$
$⇒[(x-1)(x+1)]^2+31(x-1)=0$
$⇒(x-1)^2(x+1)^2+31(x-1)=0$
$⇒(x-1)[(x-1)(x+1)^2+31]=0$
$⇒\left[ \begin{array}{l}x-1=0\\(x-1)(x+1)^2+31=0\end{array} \right. $
$⇒\left[ \begin{array}{l}x-1=0\\(x-1)(x+1)^2=-31\end{array} \right. $
$⇒\left[ \begin{array}{l}x-1=0\\(x^2-1)(x+1)=-31\end{array} \right. $
$⇒\left[ \begin{array}{l}x-1=0\\x^3+x^2-x-1=-31\end{array} \right. $
$⇒\left[ \begin{array}{l}x=1\\x∈Ф\end{array} \right. $
$⇒x=1$
