Question

已知a∧2-a-1＝0，求a∧8+7a∧-4的值

Answer 1

由a^2-a-1=0得,a^2=a+1,

于是a^4=(a+1)^2=a^2+2a+1=3a+2

a^8=(3a+2)^2=9a^2+12a+4=21a+13

a^8+7a^-4=21a+13+7/(3a+2)

=(63a^2+81a+26+7)/(3a+2)

=(63a+63+81a+33)/(3a+2)

=(144a+96)/(3a+2)

=48