a^2-a-1=0则a^8+7/a^4=

a^2-a-1=0
a^2=a+1
a^4=(a+1)^2=a^+2a+1=3a+2
a^2-a=1
a-1=1/a
所以,原式=(3a+2)^2+7(a-1)^4
=9a^2+12a+4+7(a^2-2a+1)^2
=9a^2+12a+4+7(a+1-2a+1)^2
=9a^2+12a+4+7(a^2-4a+4)
=16(a^2-a+2)
=16(1+2)
=48

a^2-a-1=0
a^2=a+1
a^4=(a+1)^2=a^2+2a+1=(a+1)+2a+1=3a+2
a^8=(a^4)^2=(3a+2)^2=9a^2+12a+4=9(a+1)+12a+4=21a+13
a^12=a^4*a^8=(3a+2)(21a+13)=63^2+81a+26=63(a+1)+81a+26=144a+89
a^8+7/a^4=(a^12+7)/a^4=(144a+89+7)/(3a+2)=(144a+96)/(3a+2)
=48(3a+2)/(3a+2)
=48