文档介绍：数学专业英语论文翻译班级:信计C123姓名:卜宏宇学号:essfulbreakthroughFrankly,inmypersonalproblem-solvingexperience,"essfill11andevenfailures,,essfulHisnotonlytotheauthorleftanegativeresult,asionallyIalwayslookforthemtocontinuetothe"problemsolvingstupid'1,Idonotknowthepersonalexperiencetosaywhetherthelaughingstockofthereadersalittlehelp,butIcanconfirmthatthisismyalreadymeagerwealthofthemainassetsofproblemsolving,andmyviews(includingArticles1998problemsolvinganalysisofserialandMIntroductiontomathematicalproblemsolvinglearning11book)hascausedsomeconcernandsympathycounterparts,needtoapologizeforthat,sometimes,ontheproblemsolvingandproblem-solvinganalysisofalargenumberofreadershavewrittenIcannotreplytoeveryone,today',ess,ess・Case1-toobtainusefulinformationfromthefailureExample1Ifa,b,carerealandunequal,andx/(a-b)=y/(b・c)=z/(c-a),seekingx+y+z・Solution:getthegeometrictheoremsx/(a-b)=y/(b-c)=z/(c-a)①=(X+y+z)/[(a-b)+(b-c)+(c-a)].②However,②thedenominatoriszero-based(a-b)+(b-c)+(c-a)=0,③Ourproblem-ment:Thisisacaseoffailedproblemsolving,[3]referredtointhesolutionafterthedirectionofsomedeal,actuallyused③,thefailureoftheprocesswasexactlythesubjectofanimpliedcondition,whichisapositivegain,essfill②style,tolookatthe(3)typeand①styleatthesametime,①stylemakeusseethecoincidenceoftwolines:xX+yY+z=0,④(A-b)X+(b-c)Y+(c-a)=0.⑤And③stylehasenabledustoseethro