已知x+y+z=o,求证x+y+z=3xyz
问题描述：
已知x+y+z=o,求证x+y+z=3xyz
答
x^3+y^3+z^3=(x+y)(x^2-xy+y^2)+z^3 =z^3-z[(x+y)^2-3xy] =z^3-z(z^2-3xy) =z^3-z^3+3xyz =3xyz
已知x+y+z=o,求证x+y+z=3xyz
x^3+y^3+z^3=(x+y)(x^2-xy+y^2)+z^3 =z^3-z[(x+y)^2-3xy] =z^3-z(z^2-3xy) =z^3-z^3+3xyz =3xyz