《比较法》参考课件2VIP免费

证明不等式的基本方法——比较法基本不等式0baba0baba0baba例1:.:,,,2233abbabababa求证且是正数已知证明:)()(2233abbaba)()(3223babbaa)()(22babbaa))((22baba2))((baba,,,baba且是正数,0)(,02baba0)()(2233abbaba即.2233abbaba3)23()23(3222xx例2:.33:2xx求证证明:xx332043)23(2x.332xx上面的证明方法称比差法其步骤是:作差--变形--判断--结论3.,,,,amaabmRabbmb例已知且求证证明:,)()(mbbabmbambma,,,,baRmba且,0,0abmb,0bambma.bambma即4,,,,.abbaabababab例已知是正数求证当且仅当时等号成立baabbaabbababababa:证明.,1,0,1,0),,(等号成立时当且仅当则不妨设不等式不变的位置交换点根据要证的不等式的特bababababababa.,,等号成立时当且仅当bababaabba练习.:,,,233255bababababa求证且是正数已知证明:)()(233255bababa)()(325235babbaa))((3322baba)())((222babababa,,,baba且是正数,0,0)(,0222babababa0)()(233255bababa).()(233255bababa练习).(23.122babba求证证明:)(2322babba222baba0)(2ba).(2322babba.222.222baba求证证明:)22()2(22baba)12()12(22bbaa0)1()1(22ba.22222baba.144,2.32aaa求证已知证明:222444144aaaaa224)2(aa0)2(,22aa04)2(22aa.1442aa.,0.4bcbacabac求证已知证明:))(()(bcaccbabcbaca,0bac,0,0,0babcac0))(()(bcaccba.bcbaca,,,,,.5adbcdcba且都是正数已知.dcdbcaba求证证明:)(dbbbcaddbcaba,,,,adbcRdcba且,0)(,0dbbbcaddbcabadbbbcad即,0)(.dcdbca同理可证.dcdbcaba补充练习:dcDdbcaCdbcaBdcdbcadbcabaadbcdcba.22..baA.)(,22,,,,,,,.1中最大的是则且都是正数已知D不能确定的大小关系是与则且若.1.1.qA.1)(1,,,1,0.2nmDqqqCqqqBqqqqqNnmqqnmnmnmnmnmnmnmA不能确定的大小关系为与则中和等差数列在等比数列D.baC,bB.abA.a)(,,0,0,.355555555313311baaabababannAabDabCbaBbabbaabbaba2.2..A.a)(2,,2,,10.42222中最大的值是则设B________,,,42,5.5222满足的条件为则实数若设baQPaaabQbaP12abab或__________,,),(log),log(log21,2log,10.621212121的大小关系是则若MQPbaMbaQbaPbaQ>P>M