已知x²+5x+1=0,求x²+1/x²,x-1/x
问题描述：
已知x²+5x+1=0,求x²+1/x²,x-1/x
答
x²+5x+1=0
x+5+1/x=0
x+1/x=-5
x²+1/x²
=(x+1/x)²-2
=(-5)²-2
=25-2
=23
(x-1/x)²
=(x+1/x)²-4
=(-5)²-4
=25-4
=21
x-1/x=±√21