已知X=[(根号5)+1]/2,试求(X^3+X+1)/X^5

网友回答

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