已知X,Y都是正实数,求证:X3+Y3大于等于X2Y+XY2

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/06 00:28:40
已知X,Y都是正实数,求证:X3+Y3大于等于X2Y+XY2
x){}K#t"_6}6clg^o|gVv%˟{HFEjGD$S]Άb++u5**+*4bF"f•AEA8#0ć<ٱ ӁɎ@v Pmv`g Ov/EsL, r%XF 1Uݶ|

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