即t??3h2(x)?2h(x)??3log22x?2log2x

2设s?log2x，则s?[1,2]，y??3log2x?2logx??3s?2s， 22ymax??5，故，t??5.

（3）由题意，得h(x)?ax?bb(x?0)，则h(x)?ax??2ab xxb?2a??8?a?28?(x?0) 2，解得?，所以h(x)?2x??x?b?8?2ab?8?假设存在最大的常数m，使h(x1)h(x2)?m恒成立.

于是设u?h(x1)h(x2)?4(x1?=

2x12?x2(x1?x2)2?2x1x26464804x1x2??16??4x1x2??16??4x1x2??32

x1x2x1x2x1x2x1x2x1x24464xx)(x2?)?4x1x2??16(1?2) x1x2x1x2x2x1

令t?x1x2，则t?x1x2?(x1?x2211)?，即t?(0,] 244801?32在t?(0,]上单调递减， 设u?4t?4t1u?u()?289，故存在最大的常数m?289

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