已知x²-16x-1=0,求x³-1\x³的值
问题描述：
已知x²-16x-1=0,求x³-1\x³的值
答
x²-16x-1=0
x-16-1/x=0
∴x-1/x=16
x³-1/x³=(x-1/x)(x²+1+1/x²)
=(x-1/x)[(x-1/x)²+3]
=16×(16²+3)
=4144