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1、257Title:SecretsinInequalitiesvolume2-advancedinequalities-freechapterAuthor:PhamKimHungPublisher:GILPublishingHouseISBN:978-606-500-002-5Copyrightc2008GILPublishingHouse.Allrightsreserved.ALLRIGHTSRESERVED.ThisbookcontainsmaterialprotectedunderInternationalandFederalCopyrightLa

2、wsandTreaties.Anyunauthorizedreprintoruseofthismaterialisprohibited.Nopartofthisbookmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recording,orbyanyinformationstorageandretrievalsystemwithoutexpresswrittenpermissionfromtheauthor/pub

3、lisher.GILPublishingHousecomenzi@gil.roPObox44,PO3Zalau,S˘alaj˘ROMANIAThisPDFisthefreepartofthebook”SecretsinInequalitiesvolume2-advancedinequalities”writtenbyPhamKimHung.ThecurrentPDFisfreeofchargeandavailableforanyonebutitisunderthecopyrightofGILPublishingHousethereforeyoucanno

4、tuseitforcommercialpurpose.258Tableofcontents1CollectedArticlesonInequalities261Article1.GENERALIZATIONOFSCHURINEQUALITY..............2621.1GeneralizedSchurInequalityforThreeNumbers.............2621.2AGeneralizationofSchurInequalityfornNumbers...........269Article2.LOOKINGATFAMIL

5、IAREXPRESSIONS................2761.3OnAM-GMInequality............................2761.4OnNesbitt’sInequality............................2841.5OnSchurInequality..............................288Article3.THOUGHTBRINGSKNOWLEDGE-VARIEDIDEAS..........2921.6ExponentSmash................

6、................2921.7UnexpectedEqualities............................2961.8UndesirableConditions...........................304Article4.CYCLICINEQUALITIESOFDEGREE3.................3101.9GettingStarted................................3101.10ApplicationforPolynomialInequalities.....

7、.............3121.11ApplicationsforFractionInequalities...................323Article5.INTEGRALANDINTEGRATEDINEQUALITES.............3291.12Gettingstarted.................................3291.13IntegratedInequalities............................332Article6.TWOIMPROVEMENTSOFTHEMIXING

8、VARIABLESMETHOD...3361.14MixingVariables