已知x^2-2x-1=0,那么x^4-6x^2+5=_数学解答

已知x^2-2x-1=0,那么x^4-6x^2+5=

人气：165 ℃　时间：2020-07-03 03:23:21

解答

x^2=2x+1,
(x^2)^2=(2x+1)^2=4x^2+4x+1,
x^4-6x^2+5
=(4x^2+4x+1)-6x^2+5
=4x^2+4x+1-6x^2+5
=-2x^2+4x+6
=-2(x^2-2x)+6
=-2+6
=4