解三次方程：x三次方+x平方-5x+3=0,求x?
问题描述：
解三次方程：x三次方+x平方-5x+3=0,求x?
答
x^3+x^2-5x+3=(x^3-x)+(x^2-4x+3)
=x(x+1)(x-1)+(x-1)(x-3)
=(x-1)(x^2+x+x-3)
=(X-1)(x^2+2x-3)
=(x-1)(x-1)(x+3)=0
x=1,-3
答
(x^3)+x^2-5x+3=0
(x^3)+2x^2-3x-x^2-2x+3=0
x（x^2+2x-3）-（x^2+2x-3）=0
（x^2+2x-3）（x-1）=0
（x+3）（x-1）（x-1）=0
∴x[1]=-3，x[2]=x[3]=1
答
x三次方+x平方-5x+3=0
x^3+x^2-2x-(3x-3)=0
x(x^2+x-2)-3(x-1)=0
x(x+2)(x-1)-3(x-1)=0
(x-1)(x^2+2x-3)=0
(x-1)(x+3)(x-1)=0
所以,方程的根为：x1=x2=1,x3=-3
答
X=1