设a=(根号5-1)/2 则(a^5 + a^4 - 2a^3 - a^2 -a +2)/(a^3 - a ) 会等于?
问题描述：
设a=(根号5-1)/2 则(a^5 + a^4 - 2a^3 - a^2 -a +2)/(a^3 - a ) 会等于?
答
a=(√5-1)/2,则a+1=(√5+1)/2,所以 a（a+1）=1
(a^5 + a^4 - 2a^3 - a^2 -a +2)/(a^3 - a )
=〔a^3(a+2)(a-1)-(a+2)(a-1)]/[(a(a+1)(a-1)]
=[(a+2)(a-1)(a^2+a+1)]/[a(a+1)]
=(√5+3)/2*(√5-3)/2*[a(a+1)+1]
=-1*2
=-2