Question

怎样解X^3-2X^2+1=0

Answer 1

配方就可以了：

X^3-2X^2+1

=x^3 - x^2 - x^2 +1

=x^2*(x-1) - (x^2-1)

=x^2(x-1) - (x+1)(x-1)

=(x-1)*(x^2-x-1)

=0

分别令x-1=0 和 x^2-x-1=0

• 得到3个根：1、1/2+√3/2  、 1/2-√3/2

Answer 2

X^3-2X^2+1=(X^3-X^2)-(X^2-1)=X^2(x-1)-(x-1)(x+1)=(x-1)(X^2-x-1)=(x-1)(x-1/2-√5/2)(x-1/2+√5/2)=0
得出每个括号内都可能为0
故X=1或X=1/2+√5/2或X=1/2-√5/2