已知X=[(根号5)+1]/2,试求(X^3+X+1)/X^5
问题描述：
已知X=[(根号5)+1]/2,试求(X^3+X+1)/X^5
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