已知x^2-2x-1=0,那么x^4-6x^2+5=

问题描述:

已知x^2-2x-1=0,那么x^4-6x^2+5=


∵x²-2x-1=0
∴x²=2x+1
∴x^4-6x^2+5
=(2x+1)²-6x²+5
=4x²+4x+1-6x²+5
=-2x²+4x+1+5
=-2(x²-2x)+6
=-2*1+6
=4

x²=1+2x
x^4-6x^2+5
=(1+2x)²-6(1+2x)+5
=1+4x+4x²-6-12x+5
=4x²-8x=4(x²-2x)=4

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