Question

设a=(根号5-1)/2 则(a^5 + a^4 - 2a^3 - a^2 -a +2)/(a^3 - a ) 会等于?

Answer 1

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