逐步降次：
a^2-a-1=o,
∴a^2=a+1,
∴a^8+7/a^4
=(a+1)^4+7/(a+1)^2
=(a^2+2a+1)^2+7/(3a+2)
=(3a+2)^2+7/(3a+2)
=9a^2+12a+4+7/(3a+2)
=21a+13+7/(3a+2)
=[(21a+13)(3a+2)+7]/(3a+2)
=(63a^2+81a+33)/(3a+2)
=(144a+96)/(3a+2)
=48.