口袋妖怪xy各种肥料:求证:(|a+b|)/(1+|a+b|)≤(|a|)/(1+|a|)+(|b|)/(1+|b|) 问题就是这个,急,谢谢~~~
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求证:(|a+b|)/(1+|a+b|)≤(|a|)/(1+|a|)+(|b|)/(1+|b|)
解详细点,谢谢了~~~~~~~~~~~~~~~~~~~~~~~~
解详细点,谢谢了~~~~~~~~~~~~~~~~~~~~~~~~
(|a+b|)/(1+|a+b|)≤(|a|)/(1+|a|)+(|b|)/(1+|b|)
证明:因为|a+b|<=|a|+|b|
|a+b|(1+|a|+|b|)<=(|a|+|b|)(1+|a+b|)
故(|a+b|)/(1+|a+b|)<=(|a|+|b|)/(1+|a|+|b|)
(|a|+|b|)/(1+|a|+|b|)=|a|/(1+|a|+|b|)+|b|/(1+|a|+|b|)
|a|/(1+|a|+|b|)<=|a|/(1+|a|)
|b|/(1+|a|+|b|)<=|b|/(1+|b|)
故|a|/(1+|a|+|b|)+|b|/(1+|a|+|b|)<(|a|)/(1+|a|)+(|b|)/(1+|b|)
故(|a+b|)/(1+|a+b|)≤(|a|)/(1+|a|)+(|b|)/(1+|b|)
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求证:(|a+b|)/(1+|a+b|)≤(|a|)/(1+|a|)+(|b|)/(1+|b|) 问题就是这个,急,谢谢~~~