解方程x³-3x²+2=0

解方程x³-3x²+2=0
解方程x³-3x²+2=0

解方程x³-3x²+2=0
x³-3x²+2=0
x³-x²-(2x²-2)=0
x²(x-1)-2(x+1)(x-1)=0
(x-1)(x²-2x-2)=0
x-1=0 或x²-2x-2=0
x=1或x²-2x+1=3
(x-1)²=3
x-1=±√3
于是
x1=1+√3 x2=1-√3 x3=1

x³-3x²+2=x³-x²-2x²+2=(x-1)x²-2(x-1)(x+1)=(x-1)(x²-2x-2)=0
x=1 x=1+根号3，x=1-根号3

x³-3x²加2
=x³-1-3x²加3
=(x-1)(x²加x加1)-3(x加1)(x-1)
=(x-1)(x²-2x-2)