问题标题:
【一些比较难的英文数学题(追加20分)1.Apolynomialp(x)satisfiesp(5−x)=p(5+x)forallrealx.Supposep(x)=0hasfourdistinctrealroots.Findthesumoftheseroots.2.Apersoncashesacheckatabank.Bymistakethetellerpa】
问题描述:

一些比较难的英文数学题(追加20分)

1.Apolynomialp(x)satisfiesp(5−x)=p(5+x)forallrealx.Supposep(x)=0hasfour

distinctrealroots.Findthesumoftheseroots.

2.Apersoncashesacheckatabank.Bymistakethetellerpaysthenumberofcentsas

dollarsanddollarsascents.Thepersonspends$3.50beforenoticing,thenlaterfindsthattheremainingmoneyisexactlydoubletheamountofthecheck.Whatwastheamount?

3.Leta,b,cbeintegerssuchthat2005dividesbothab+9b+81andbc+9c+81.Provethat2005alsodividesca+9a+81.

4.Twothievesstoleanopenchainwith2kwhitebeadsand2mblackbeads.Theywanttosharethelootequally,bycuttingthechaininpiecesinsuchawaythateachonegetskwhitebeadsandmblackbeads.Whatistheminimumnumberofcutsthatissufficient?Describeanalgorithmtomakethecuts.

5.LetABCDbeaunitsquareandmarkoffpointsE,F,G,HsuccessivelyinsidesAB,BC,CD,DA

sothatAE=BF=CG=DH=2011/2012.ProvethattheregionthatistheintersectionoftrianglesAGB,BHC,CED,DFAisasquarewitharea

1/(20112+20122)^2.

畅玉明回答:
  既然你问到这么难的问题,我就直接用英文了,名词什么的我想你也应该懂的.1.sincep(5−x)=p(5+x),wecantellthatp(x)isanevenfunction,andissymmetricaroundyaxis.Fromthepropertiesofev...
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《【一些比较难的英文数学题(追加20分)1.Apolynomialp(x)satisfiesp(5−x)=p(5+x)forallrealx.Supposep(x)=0hasfourdistinctrealroots.Findthesumoftheseroots.2.Apersoncashesacheckatabank.Bymistakethetellerpa】|高中数学问答-字典翻译问答网》
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