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落叶无声===

木虫 (正式写手)

Dragonborn

[求助] 求助数学证明题

求证: n*(1-x^2)*x^(2n)-(2x+x^2)*(1-x^2n)+2x*(1+x)*(1-x^n)恒大于0,其中0<x<1,n为大于2的整数。求大神指教!不胜感激!由于手机传不了图,只能手打。

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落叶无声===

木虫 (正式写手)

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引用回帖:
4楼: Originally posted by zaq123321 at 2015-03-24 19:48:30
Sorry about this. Then should we compute the second derivative, which is negative in (0,1)?
But the calculation looks pretty complex....

求导也算过,但是太复杂了,也判断不出式子单调性。因式分解尝试分解了一下,但是没有进一步进展
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5楼2015-03-24 20:38:37
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zaq123321

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【答案】应助回帖

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感谢参与,应助指数 +1
落叶无声===: 金币+10, ★有帮助, 非常谢谢你能关注这个问题! 2015-03-26 01:42:30
Replace the second x^(2n) with x^n. Combine the second term and third term. Then each term is positive.
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2楼2015-03-24 15:56:57
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落叶无声===

木虫 (正式写手)

Dragonborn

引用回帖:
2楼: Originally posted by zaq123321 at 2015-03-24 15:56:57
Replace the second x^(2n) with x^n. Combine the second term and third term. Then each term is positive.

替换后式子被放大了吧……要放缩的话应该要放小……不过还是感谢!

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3楼2015-03-24 18:00:34
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zaq123321

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引用回帖:
3楼: Originally posted by 落叶无声=== at 2015-03-24 18:00:34
替换后式子被放大了吧……要放缩的话应该要放小……不过还是感谢!
...

Sorry about this. Then should we compute the second derivative, which is negative in (0,1)?
But the calculation looks pretty complex.
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4楼2015-03-24 19:48:30
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