x+y-x=0求证x^3+8y^3=z^3-6xyz

问题描述:

x+y-x=0求证x^3+8y^3=z^3-6xyz

z=x+y
z^3-6xyz
=(x+y)^3-6xy(x+y)
=x^3+3x^2y+3xy^2+y^3-6x^2y-6xy^2
=(x-y)^3
只能推到这里,
x^3+8y^3=z^3-6xyz
随便带入 就知道不成立