复数的因式分解 x^6-y^6

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/19 08:37:27
复数的因式分解x^6-y^6复数的因式分解x^6-y^6复数的因式分解x^6-y^6x^6-y^6=(x^3+y^3)(x^3-y^3)=(x+y)(x-y)(x^2+xy+y^2)(x^2xy+y^

复数的因式分解 x^6-y^6
复数的因式分解 x^6-y^6

复数的因式分解 x^6-y^6
x^6-y^6
=(x^3+y^3)(x^3-y^3)
=(x+y)(x-y)(x^2+xy+y^2)(x^2xy+y^2)
=(x+y)(x-y)(x^2+xy+y^2/4+3*y^2/4)(x^2-xy+y^2/4+3*y^2/4)
=(x+y)(x-y)((x+y/2)^2+3*y^2/4)((x-y/2)^2+3*y^2/4)
=(x+y)(x-y)(x+y/2-√3yi/2)(x+y/2+√3yi/2)(x-y/2-√3yi/2)(x-y/2+√3yi/2)