首页 / 是否存在常数 c，使得不等式对任意正数 x,y恒成立？

是否存在常数 c，使得不等式对任意正数 x,y恒成立？

是否存在常数 c，使得不等式对任意正数 x,y恒成立？

答案

解析：令x=y得，故猜想c=,下证不等式恒成立。

要证不等式，因为x,y是正数，即证3x(x+2y)+3y(2x+y)≤2（2 x+y）(x+2y),也即证,即2xy≤，而此不等式恒成立，同理不等式也成立，故存在c=使原不等式恒成立。

相关题目

91.You will find as you read fiats book that you just can’t keep some of these
91.You will find as you read fiats book that you just can’t keep some of these stones to ______. You will want to share them with a friend.  A. itself                     B. yo
(+)2dx= . 
(+)2dx= . 
下列各组词语中加点的字，每对的读音都不相同的一组是（ 
下列各组词语中加点的字，每对的读音都不相同的一组是（  ） A．朔风/上溯果脯/哺育真谛/取缔 B．惆怅/绸缪      简陋/露面      威名/偎依 C．
Roger Federer and Serena Williams have been named as 2009' s world champions by
Roger Federer and Serena Williams have been named as 2009' s world champions by the International Tennis Federation（ITF） after topping the year-end rankings．          Federer, who wins t
鸦片最早用于药物（有止痛、止泻、止咳的作用），长期服
鸦片最早用于药物（有止痛、止泻、止咳的作用），长期服用会成瘾。现有鸦片的替代品用于脱瘾治疗，结构简式如图所示：。1 mol该化合物与足量的NaO
Included _____. A. all kinds of books            B. was all kinds of b
Included _____. A. all kinds of books            B. was all kinds of books C. were all kinds of books           D. all kinds of books are
—How long have you ______ Jinan?     —For ten years.     A. moved to
—How long have you ______ Jinan?     —For ten years.     A. moved to           B. left for          C. lived in        D. gone to
This was no ordinary class. The students who came together were all science or e
This was no ordinary class. The students who came together were all science or engineering professors at Cornell University. They had interrupted their research to accept an invitation to take part in

最新题目

对于反应：2H2S+SO2===3S +2H2O，被氧化的硫原子与被还原的硫原
如图，已知AC=BD,要使△ABC≌△DCB，只需增加一个条件是    
.  I have repaired much of the equipment. Would you please help me with _______
氢气(H2)、一氧化碳(CO)、辛烷(C8H18)、甲烷(CH4)的热化学方程式
A couple in South Carolina has been eagerly seeking an organ donor. They haven
达·芬奇是意大利文艺复兴时期的巨匠，他多才多艺，在艺术
More than one student in our class _________ to Shanghai Expo.       A．ha
橘中含有对人体有益的柠檬烯．若用R表示柠檬烯，其完全燃
《宋书·志序》载：“自戎狄内侮，有晋东迁，中土遗氓，播
依次填入下列横线处的词语，最恰当的一组是( ) ①司马迁的
.如图所示，线段AC和BD交于O点，且OA=OC，AE∥FC，BE=FD，则图中
对下列细胞分裂模式图的分析，正确的是（   ）   A．分别
       For many years scientists have said that the earth is getting warm
平面直角坐标系中，抛物线交轴于A、B两点（点A在点B左侧）
 There is some doubt among people __________ $750 is too much for an iPhone 6
 17.  We got to the airport early,_____missing our flight. A.  in case of  
复数的值是   （   ）     A．－    B．      C．    D．
下列数剧中与实际相符的是 A．中学生脚的长度为50cm     
某反应过程中体系的能量变化如图所示，下列说法错误的是(