已知√5+1/2=a求a^5+a^3+a+1/a^6的值
问题描述：
已知√5+1/2=a求a^5+a^3+a+1/a^6的值
答
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 ....