解方程x^3+2x^2-5x+2=0
问题描述：
解方程x^3+2x^2-5x+2=0
答
x^3+2x^2-5x+2
=x^3-x^2+3(x^2-x)-2(x-1)
=x^2(x-1)+3x(x-1)-2(x-1)
=(x^2+3x-2)(x-1)
=((x+3/2)^2-17/4)(x-1)
=(x+(3+√17)/2))(x+(3-√17)/2)(x-1)
=0
所以x=(3+√17)/2 或x=(3-√17)/2 或x=1
答
(x^3-x)+(2x^2-4x+2)=x(x+1)(x-1)+2(x-1)^2=(x-1)(x^2+x+2x-2)=(x-1)(x^2+3x-2)=0
x=1,x=(-3+根号17)/2,x=(-3-根号17)/2.
请采纳！
答
x^3+2x^2-5x+2=0
x^3-1+2x^2-5x+3=0
(x-1)(x^2+x+1)+(2x-3)(x-1)=0
(x-1)(x^2+x+1+2x-3)=0
(x-1)(x^2+3x-2)=0
(x-1)(x^2+3x+9/4-9/4-2)=0
(x-1)[(x+3/2)^2-17/4]=0
(x-1)(x+3/2-√17/2)(x+3/2+√17/2)=0
x=1或x=√17/2-3/2或x=-√17/2-3/2