已知a满足等式a²-a-1=0，求代数值a^8+7a^(-4)的值？
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a^2=a+1
a^4=(a^2)^2=(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^8*a^4=(3a+2)(21a+13)=63a^2+81a+26=63(a+1)+81a+26=144a+89
a^8+7a^-4
=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
a^4=(a^2)^2=(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^8*a^4=(3a+2)(21a+13)=63a^2+81a+26=63(a+1)+81a+26=144a+89
a^8+7a^-4
=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
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