$x ³+7x-8=0$
$(=)x³-x+8x-8=0$
$(=)x(x²-1)+8(x-1)=0$
$(=)x(x-1)(x+1)+8(x-1)=0$
$(=)(x-1)[x(x+1)+8)=0$
$(=)(x-1)(x²+x+8)=0$
$(=)\left[ \begin{array}{l}x-1=0\\x²+x+8=0\end{array} \right.(=)\left[ \begin{array}{l}x=1\\x²+x=-8=)\text{Vô lý}\end{array} \right. $
$S=\text{{1}}$