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黑夜 · 发表于 2008-9-8 21:09:00

1. X^4+Y^4>Z^4？

条件1：X^2+Y^2>Z^2

条件2：X+Y>Z

2. PS:ABC is a triangle. D is the midpoint of BC. E is the midpoint of AC while F is midpoint of EC. If area of triangle ABC is 24. What is the area for triangle DEF? 3

请高人指点下。。。希望能写写分析的过程~~~~~

[此贴子已经被作者于2008-9-8 21:08:59编辑过]

TCTC · 发表于 2008-9-8 21:25:00

以下是引用黑夜在2008-9-8 21:09:00的发言：

1. X^4+Y^4>Z^4？

条件1：X^2+Y^2>Z^2

条件2：X+Y>Z

2. PS:ABC is a triangle. D is the midpoint of BC. E is the midpoint of AC while F is midpoint of EC. If area of triangle ABC is 24. What is the area for triangle DEF? 3

请高人指点下。。。希望能写写分析的过程~~~~~

1.条件1举个反例：X^2=Y^2=1/2 z^2=3/4

条件2举个反例：x=-1 Y=-1 z=-2.5

2.S(DEF)=1/2AB*1/2DC*1/2=1/8*AB*DC=1/8*24=3

yumikochien · 发表于 2008-9-8 22:06:00

问X^4+Y^4>Z^4？
条件1：X^2+Y^2>Z^2
条件2：X+Y>Z

我觉得选E，可是为什么不选C又举不出例子来，脑子浆特勒。。。

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