已知x²-5x-1=0,则x²-4x-(1/x)=?

问题描述:

已知x²-5x-1=0,则x²-4x-(1/x)=?

x²-5x-1=0
x²=5x+1
x²-5x-1=0
x-5-1/x=0
x - 1/x = 5
x²-4x-(1/x)
= 5x+1 - 4x - 1/x 【∵x²=5x+1】
= x-1/x +1
=5+1 【∵x - 1/x = 5】
= 6