x+y+z=0.则X3+Y3+Z3=?（X的三次方加Y的三次方加Z的三次方等于多少?）为什么?

Question

x+y+z=0.则X3+Y3+Z3=?（X的三次方加Y的三次方加Z的三次方等于多少?） 为什么?

Answer 1

x+y+z=0,
则z=-(x+y),
x^3+y^3+z^3
=x^3+y^3-(x+y)^3
=x^3+y^3-(x^3+y^3+3x^2y+3xy^2)
=-3xy(x+y)
=3xyz