已知：a=2分之3加根号5,求：a的5次幂分之a立方+a的平方+1的值

已知:A=(3+根号5)/2,求(A^3+A^2+1)/A^5
(A^3+A^2+1)/A^5=A^3/A^5+A^2/A^5+1/A^5
=1/A^2+1/A^3+1/A^5
=(1/A)^2+(1/A)^3+(1/A)^5
(1/A)^2=[2/(3+根号5)]^2=(3-根号5)/2
(1/A)^3=[(3-根号5)/2]*[2/(3+根号5)]
=(7-3倍根号5)/2
(1/A)^5=[(3-根号5)/2]*[(7-3倍根号5)/2]
=(9-4倍根号5)/2
所以原式=(19-8倍根号5)/2