已知x^2-16x-1=0,求x^3-1/x^3的值
问题描述：
已知x^2-16x-1=0,求x^3-1/x^3的值
答
x^2-16x-1=0
x-16-1/x=0
x-1/x=16
x^2+1/x^2=(x-1/x)^2+2=256+2=258
x^3-1/x^3=(x-1/x)(x^2+1/x^2+1)=16*259=4144
答
由条件知,x-1/x=16,所以x^3-1/x^3=(x-1/x)^3+3(x-1/x)=4048
答
x^2-16x-1=0
x^2-x=16x 两边除x
x-1/x=16 平方
x^2-2+1/x^2=256
x^2+1/x^2=258
(x^2+1/x^2)(x-1/x)
=x^3-x+1/x-x^3=258*16=4128
x^3-1/x^3=4128+x-1/x=4128+16=4144