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【存档】2014年美国数学奥林匹克(含强神解答)

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1楼2015-01-25 18:18回复
    519357823
    国家队13



    第二题看不清的看这一楼



    2楼2015-01-25 18:19
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      自己的6做法【个人觉得这个比走向好130倍】
      6


      3楼2015-01-25 18:19
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        4


        ,6




        4楼2015-01-25 18:20
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          1、Using Vieta we get that the relation equals

          where . And so the maximum value is , achieved when the polynomial is ().


          5楼2015-01-25 18:21
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            3、Replace the condition by . Then if , a nice solution would involve polynomials. We get that if then . Then we see . So a nice solution would involve . Then we expand and see that , works. So we're done


            6楼2015-01-25 18:21
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