已知√5+1/2=a求a^5+a^3+a+1/a^6的值

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已知√5+1/2=a求a^5+a^3+a+1/a^6的值已知√5+1/2=a求a^5+a^3+a+1/a^6的值已知√5+1/2=a求a^5+a^3+a+1/a^6的值已知,(√5+1)/2=a,可得

已知√5+1/2=a求a^5+a^3+a+1/a^6的值
已知√5+1/2=a求a^5+a^3+a+1/a^6的值

已知√5+1/2=a求a^5+a^3+a+1/a^6的值
已知,(√5+1)/2 = a ,
可得:
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 ,
所以,
(a^5+a^3+a+1)/a^6 = (8a+5)/(8a+5) = 1 .