Question

解方程，求详细过程

r^3-3r+2=0

Answer 1

很容易就可以观察出来此方程有一个根为1，故有个r-1的因子，分解因式可得：（r-1)(r*r+r-2)=0进一步分解可得：（r-1)（r-1)(r+2)=0，故三个根分别为：1，1，-2

Answer 2

r^3-3r+2=0
r^3-1-3r+3=0
(r-1)(r^2+r+1)-3(r-1)=0
(r-1)(r^2+r-2)=0
(r-1)^2(r+2)=0
r-1=0或r+2=0
r=1或r=-2

Answer 3

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

(r-1)（r^2+r-2)=0
(r-1)(r-1)(r+2)=0
r=1,r=-2

Answer 4

r=-2

Answer 5

r^3-3r+2=0
r^3-r^2+r^2-r-2r+2=0
r^2(r-1)+r(r-1)-2(r-1)=0
(r-1)(r^2+r-2)=0
(r-1)(r-1)(r+2)=0
r1=r2=1
r3=-2