已知n^2-n-1=0,则n^3-n^2+5=?
问题描述：
已知n^2-n-1=0,则n^3-n^2+5=?
答
n^2-n-1=0
n²-n=1
n^3-n^2+5
=n(n²-n)+5
=n+5
∵n²-n=1
n²-n+1/4=1+1/4
(n-1/2)²=5/4
n-1/2=±（√5）/2
n=(1±√5)/2
∴n^3-n^2+5
=n+5
=(1±√5)/2+5
=(11±√5)/2