已知根号5+1分之2=a,求a的5次方+a的3次方+a+1分之a的6次方的值?

Question

已知根号 5+1分之2=a ,求 a的5次方+a的3次方+a+1分之a的6次方 的值?

Answer 1

(√5+1)/2 = a ,
a-1/2 = √5/2 ,
(a-1/2)^2 = 5/4 ,
a^2 = a+1 ,
a^3 = a^2+a = 2a+1 ,
a^4 = 2a^2+a = 3a+2 ,
a^5 = 3a^2+2a = 5a+3 ,
a^6 = 5a^2+3a = 8a+5 ,
a^6/(a^5+a^3+a+1) = (8a+5)/(8a+5) = 1 .