2x^3-3x^2+1=0 x=?

来源:百度知道 编辑:UC知道 时间:2024/05/14 06:42:51

(2x^3-2)-(3x^2-3)=0
2(x-1)(x^2+x+1)-3(x+1)(x-1)=0
(x-1)(2x^2+2x+2-3x-3)=0
(x-1)(2x^2-x-1)=0
(x-1)(2x+1)(x-1)=0
(x-1)^2(2x+1)=0
x=1,x=-1/2

1

2x³-3x+1=0
根据观察,有一个根是x=1,然后利用整法,分解因式得
(x-1)(2x²+2x-1)=0
解得,x=1或x=[-1±根号3]/2

2x^3-3x^2+1
=2x^3-2x^2-x^2+1

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

得:x=-1/2或者1