(X三次方)—(2X二次方)+1=0的解

问题描述:

(X三次方)—(2X二次方)+1=0的解

x^3-2x^2+1
=[(x^3)-1]-2(x²-1)(把1拆成-1+2)
=(x-1)(x²+x+1)-2(x+1)(x-1)
=(x-1)(x²-x-1) (因式分解)
∴(x-1)(x²-x-1)=0
∴x=1,x=(1+√5)/2,x=(-1+√5)/2.