已知x+y>0,比较x^3+y^3与x^2y+xy^2的大小
答案:2 悬赏:20
解决时间 2021-10-20 03:13
- 提问者网友:王者佥
- 2021-10-19 19:49
同题
最佳答案
- 二级知识专家网友:逐風
- 2019-09-12 05:21
已知x+y>0,比较x^3+y^3与x^2y+xy^2的大小
解x^3+y^3-(x^2y+xy^2)
=x^3-x^2y+(y^3-xy^2)
=x^2(x-y)-y^2(x-y)
=(x^2-y^2)(x-y)
=(x+y)(x-y)(x-y)
=(x+y)(x-y)^2≥0
所以x^3+y^3-(x^2y+xy^2)≥0
所以x^3+y^3≥x^2y+xy^2
解x^3+y^3-(x^2y+xy^2)
=x^3-x^2y+(y^3-xy^2)
=x^2(x-y)-y^2(x-y)
=(x^2-y^2)(x-y)
=(x+y)(x-y)(x-y)
=(x+y)(x-y)^2≥0
所以x^3+y^3-(x^2y+xy^2)≥0
所以x^3+y^3≥x^2y+xy^2
全部回答
- 1楼网友:走死在岁月里
- 2021-02-13 22:49
答案:0
解题过程如下:
x^3+x^2y+xy^2+y^3=(x^3+x^2y)+(xy^2+y^3)
=x^2(x+y)+y^2(x+y)
=(x+y)(x^2+y^2)
因为x+y=0,所以原式=0
谢谢采纳,呵呵
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