已知x>y,求证x3一y3>x方y一xy方

问题描述:

已知x>y,求证x3一y3>x方y一xy方

x3一y3=(x-y)(x方+xy+y方)
x方y一xy方=xy(x-y)
x方+xy+y方>xy
x>y则x-y>0
因此(x-y)(x方+xy+y方)>xy(x-y)
所以
x3一y3>x方y一xy方