Question

已知X=[(根号5)+1]/2,试求(X^3+X+1)/X^5

Answer 1

x=(√5+1)/2

x^2=(3+√5)/2

1/x=2/(√5+1)=(√5-1)/2

1/x^2=(5+1-2√5)/4=(3-√5)/2

x^3/(x^3+x+1)

=x/(x+1/x+1/x^2)

=x/[(√5+1)/2+(√5-1)/2+(3-√5)/2]

=x/[(3+√5)/2]

=x/x^2

=1/x

=(√5-1)/2