本科畢業(yè)論文（2010屆）題目數(shù)形結(jié)合思想在解題中的應(yīng)用學(xué)院數(shù)學(xué)與信息工程學(xué)院專業(yè)數(shù)學(xué)與應(yīng)用數(shù)學(xué)班級(jí)2006級(jí)數(shù)學(xué)班學(xué)號(hào)學(xué)生姓名指導(dǎo)教師完成日期2010年5月I摘要數(shù)形結(jié)合是數(shù)學(xué)研究和學(xué)習(xí)中的重要思想和解題方法，用數(shù)形結(jié)合方法可以使復(fù)雜問題簡單化、抽象問題具體化；能夠變抽象的數(shù)學(xué)語言為直觀的圖形、抽象思維為形象思維，有助于把握數(shù)學(xué)問題的本質(zhì)。所謂數(shù)形結(jié)合就是根據(jù)數(shù)學(xué)問題的條件和結(jié)論之間的內(nèi)在聯(lián)系分析其代數(shù)含義，又揭示其幾何直觀，使數(shù)量關(guān)系與空間形式和諧結(jié)合在一起的方法。通過“以形助數(shù)”和“以數(shù)輔形”這兩大題型的具體分析，揭示出“數(shù)”與“形”之間的緊密關(guān)系，從而把問題優(yōu)化，獲得解決。關(guān)鍵詞數(shù)形結(jié)合線性規(guī)劃數(shù)量關(guān)系IIABSTRACTCOMBININGTHEOPERATIONWITHFIGUREISTHESTUDYOFMATHEMATICSANDLEARNINGTHEIMPORTANTTHINKINGANDPROBLEMSOLVINGMETHODS,WHICHCANSIMPLIFYCOMPLICATEDPROBLEMS,SPECIFYTHEABSTRACTONES,ANDTURNTHEABSTRACTSHAPESANDTHOUGHTTOBEVISUAL,ANDISACCORDINGLYHELPFULTOGRASPTHEESSENCEOFMATHEMATICSTHESOCALLEDCOMBINATIONISANAPPROACH,WHICHNOTONLYANALYZEMEANINGOFALGEBRA,BUTALSODISCLOSETHESIGNIFICANCEOFGEOMETRYACCORDINGTOTHEINSIDERELATIONSHIPOFCONDITIONSANDCONCLUSIONS,ANDHARMONIOUSLYCOMBINESTHEFORMOFNUMBERANDSPACEASONETHISARTICLEWILLSETFORTHTHETIGHTCONTACTBETWEENALGEBRAANDGEOMETRYTHROUGHOUTTHEANALYSISOFTWOTYPICALSTYLES“GEOMETRYHELPSUNDERSTANDALGEBRA”AND“ALGEBRAHELPSUNDERSTANDGEOMETRY”,INORDERTOSOLVERELEVANTPROBLEMSWELLKEYWORDSTHECOMBINATIONOFALGEBRAANDGEOMETRYTHELINEARPROGRAMMINGQUANTITATIVERELATIONSHIPIII目錄1引言12以形助數(shù),代數(shù)問題幾何化221以形助數(shù)解決集合問題222以形助數(shù)解決取值范圍問題323以形助數(shù)解決解含參數(shù)問題424以形助數(shù)解決不等式問題G252G24以形助數(shù)G8726G2001數(shù)G7509值G252G25以形助數(shù)在解析幾何中的G5224用G262G26G1523助于復(fù)G5191G19766G990的G9869解決復(fù)數(shù)問題G273G714以數(shù)輔形,幾何問題代數(shù)化G2731用代數(shù)方法解決G5191G19766幾何問題G2732用代數(shù)方法解決G12447體幾何的問題G28參G13783G7003G1049811G16886G17778121數(shù)形結(jié)合思想在解題中的應(yīng)用APPLICATIONOFTHEFIGUREANDSHAPECOMBINATIONINSOLVINGPROBLEMS1引言A2A0A1A3A4A5A6A7A2A8A9A10A11A12A13A14A15A16A17A18A19A20A7A21A22A25A26A2A11A14A23A24A27A28A10A25A31A23A29A1A24A27A30A32A7A35A36A33A34A7A2A8A9A10A37A12A13A14A15A38A39A40A41A42A43A25A46A44A36A2A8A9A10A30A32A45A47A14A7A48A51A33A34A25A46A44A36A47A14A7A48A51A30A32A45A2A8A9A10A33A34A25A29A1A49A50A52A53A22A7A2A0A33A34A54A55A32A58A59A56A32A25A61A57A60A53A22A62A63A17A14A22A62A63A64A65A66A67A33A34A7A62A68A37A69A70A71A23A2A14A38A39A7A62A68A69A70A35A74A72A2A0A73A75A76A77A25A80A78A72A79A8A81A79A58A84A82A11A83A82A7A85A86A87A25A71A36A2A11A14A28A10A40A41A88A35A91A92A89A90A76A77A25A10A93A94A95A96A88A97A98A33A34A99A2A32A7A69A70A25A102A99A2A15A100A101A50A52A97A98A103A104A25A36A47A14A105A13A7A97A98A9A10A106A107A45A99A2A15A105A13A7A99A2A9A10A35A110A108A5A109A111A112A113A25A70A92A2A0A114A115A116A117A1A118A119A17A120A121A25A72A122A37A2A21A105A13A58A69A86A37A123A124A105A13A125A126A40A41A21A127A9A10A25A102A99A2A69A70A19A20A97A98A33A34A25A130A26A128A126A88A132A129A97A98A0A35A134A41A25A97A98A0A87A131A133A81A77A135A61A132A136A7A33A34A25A139A137A138A140A141A142A143A144A58A126A69A145A82A58A32A146A17A69A140A33A34A25A149A147A31A148A150A151A99A2A69A70A152A153A88A154A155A7A132A136A35A158A49A72A156A99A11A3A99A2A0A7A19A20A87A25A97A98A33A34A7A99A2A32A31A23A157A159A160A161A7A69A70A162A163A25A166A164A165A167A7A127A102A35A170A168A2A37A14A7A169A72A28A10A25A135A171A49A97A98A0A172A152A88A99A2A32A7A166A173A174A175A25A31A49A131A133A99A2A0A11A2A0A141A129A7A176A34A175A166A88A177A178A7A54A55A48A25A72A2A0A132A34A87A25A181A102A2A14A38A39A62A68A25A71A23A179A180A33A34A7A175A83A182A14A25A46A44A36A47A14A48A51A33A34A30A32A45A2A8A9A10A41A19A20A25A134A44A36A2A8A9A10A33A34A30A32A45A47A14A48A51A41A19A20A25A1A183A1A2A150A14A46A1A14A150A2A25A49A2A0A33A34A184A185A32A58A53A22A33A34A175A83A32A35A2A0A0A186A87A25A135A185A187A23A2A7A188A189A37A14A7A19A20A25A192A133A7A23A102A2A14A38A39A62A68A132A34A35A193A190A191A194A195A85A198A199A2A0A23A19A20A3A4A5A6A7A8A7A9A10A37A12A13A14A15A7A196A0A35A201A2A14A38A39A71A23A179A180A2A0A33A34A7A159A202A11A38A197A105A13A7A169A72A28A10A25A204A141A129A18A99A2A143A200A25A206A203A205A18A97A98A54A55A25A49A2A8A9A7A207A208A209A210A37A12A13A14A15A7A54A55A14A22A211A212A58A11A213A94A38A39A72A157A40A25A216A141A214A102A64A65A38A39A25A218A215A132A34A62A217A25A49A33A34A32A2192A17A220A58A32A221A17A184A25A130A26A152A153A132A136A35A224A151A49A102A88A2A14A38A39A7A69A70A25A225A133A33A34A183A222A223A26A132A25A228A132A70A184A226A230A199A2A201A37A199A14A201A23A157A21A227A229A25A233A231A13A232A234A235A135A23A199A2A201A11A199A14A201A7A227A229A7A93A157A35A238A236A237A239A59A195A85A198A199A2A240A14A76A241A54A55A25A14A241A2A76A219A242A243A25A2A14A38A39A244A245A246A25A249A247A141A114A232A248A250A35A201A127A102A2A251A252A253A254A255A16A0A1A2A3A4A5A124A198A20A6A25A1A2A253A7A251A8A9A10A11A12A50A25A13A14A15A10A17A255A8A9A18A19A21A58A22A23A10A253A24A17A255A25A8A9A26A134A10A17A255A27A28A11A12A10A29A20A30A25A1A2A31A32A199A253A201A10A33A34A50A35A199A251A201A10A36A84A50A25A37A38A39A40A41A124A42A253A17A255A25A8A9A18A43A251A134A0A44A45A199A253A201A10A33A34A50A25A46A61A47A48A49A34A252A210A51A166A54A17A255A52A53A27A10A43A251A55A56A6A25A0A163A57A55A59A10A60A62A63A48A64A27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