已知x²-5x-1=0,则x²-4x-(1/x)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/10 06:54:01

已知x²-5x-1=0,则x²-4x-(1/x)=?
已知x²-5x-1=0,则x²-4x-(1/x)=?

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

因为x²-5x-1=0,所以x^2-4x=x+1,x^2=5x+1
故x²-4x-(1/x)
=x+1-1/x
=(x^2+x-1)/x
=(5x+1+x-1)/x
=6x/6