Question

在复数范围内分解因式:x^4+x^2*y^2+y^4

Answer 1

x^4+x^2*y^2+y^4

=x^4+2x^2*y^2+y^4-x^2*y^2

=(x^2+y^2)^2-(xy)^2

=(x^2+xy+y^2)(x^2-xy+y^2)

[

x^2+xy+y^2=0的解为 x=y*(-1±√3i)/2

x^2-xy+y^2=0的解为 x=y*(1±√3i)/2

]

=(x-y*(-1+√3i)/2)(x-y*(-1-√3i)/2)(x-y*(1+√3i)/2)(x-y*(1-√3i)/2)