已知X,Y都是正实数,求证:X3+Y3大于等于X2Y+XY2

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已知X,Y都是正实数,求证:X3+Y3大于等于X2Y+XY2已知X,Y都是正实数,求证:X3+Y3大于等于X2Y+XY2已知X,Y都是正实数,求证:X3+Y3大于等于X2Y+XY2x3+y3-(x2y

已知X,Y都是正实数,求证:X3+Y3大于等于X2Y+XY2
已知X,Y都是正实数,求证:X3+Y3大于等于X2Y+XY2

已知X,Y都是正实数,求证:X3+Y3大于等于X2Y+XY2
x3+y3-(x2y+xy2)
=x2(x-y)-y2(x-y)
=(x-y)(x2-y2)
=(x-y)(x+y)(x-y)
=(x-y)^2(x+y)
因为X,Y都是正实数
则x+y>0 (x-y)^2>=0
所以x3+y3-(x2y+xy2)>=0
x3+y3>=x2y+xy2