Question

x^3-2x^2+1=0解这个方程

要有具体步骤

Answer 1

x^3-2x^2+1=0
(x^3-x^2)-(x^2-1)=0
x^2(x-1)-(x+1)(x-1)=0
(x-1)(x^2-x-1)=0
x-1=0或x^2-x-1=0
x=1
x^2-x-1=0用求根公式求
x=(1±√5)/2
所以x=1或x=(1±√5)/2

Answer 2

x^3-2x^2+1=0
x(x^2-2x)+1=0 (提出x)
x(x^2-2x+1)-x+1=0 (括号内配方）
x(x^2-2x+1)=x-1 (移向）
x(x-1)^2=x-1
x-1=0
x=1
x(x-1)=1
x^2-x=1
x^2-x-1=0
用求根公式：x=(-b±√△)/2a (a=1 ,b=-1 ,c= -1)
得x=(1±√5)/2
或者x=1

Answer 3

x^3-2x^2+1=0
x^3-x^2-x^2+1=0
x^2(x-1)-(x^2-1)=0
x^2(x-1)-(x+1)(x-1)=0
(x^2-x-1)(x-1)=0
方程解为x=1或x=（1±√5）/2

Answer 4

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

Answer 5

(x-1)*(x^2-x-1)=0
x=1
x=(1+5^0.5)/2
x=(1-5^0.5)/2