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)
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)