若x²+x+1=0,则x^4-x²-2x-1=____.

若x²+x+1=0,则x^4-x²-2x-1=____.
若x²+x+1=0,则x^4-x²-2x-1=____.

若x²+x+1=0,则x^4-x²-2x-1=____.
x²=-x-1
两边平方
x^4=x²+2x+1
所以原式=x²+2x+1-x²-2x-1=0

x^4-x²-2x-1 = x^4-(x+1)^2=(x^2+x+1)(x^2-x-1) = 0*)(x^2-x-1) = 0

x^4+x^2-2x-1=x^4-(x^2+2x+1)=x^4-(x+1)^2=(x^2+x+1)(x^2-x-1)=0