【解题思路】本题可通过求函数的最大值来证明。证明：设[tex=10.143x1.571]9Rqj7Q7yHRlDqosUV6cmybnW0GRdr4mwH9dmkA5rLZM0xD0TXuNVMe1jwx5LyoLvBQDVYaEqtEdtOMG+lONFpg==[/tex]，由题设[tex=5.714x1.5]wexgr6BjbEMq9oe2tZkPwIrcyGSUkrvOAF5mMq7kB5c=[/tex]，而[tex=2.357x1.357]JUTEIsqYTDc5LuGJ9BwPLIFiVShiflnznzs3pBQqDnM=[/tex]，故[tex=1.571x1.0]TYvJVTKRr6FnfPb2CtQh4Q==[/tex]应满足[tex=8.0x1.429]wexgr6BjbEMq9oe2tZkPwPF4n2dqfV7L9QwU6XA14RQCV6xmyTE2IZVeCUVmUPZgrHr15EBqpql4uKvt9bI6Og==[/tex]为边界。因为[tex=12.857x3.643]GE56u9QCDTqcLxZ66HADyl8dF7kvj0x6YvfD2BU2UT/I7bWEmXjIY88776zL9BAOTNSjx07cIZ0uTUb0BdCGeJPwikPuKPCZfwiQ15eNsxWSVXEUPMTT3AgtI6qksA77w8EmG4amRyRMGi3pWNrLmky2uEkJNf0MR/1MM2w0XPbGm3sgNZJp23jyJu2Xz4ND6S+NgldxhddpwAKRxCEdlQQyKhRJjGST10rJiByKSxlLR8tnPptT5xmKiioQrem2htl/XgdJOpo6qnhSu5NeEg==[/tex]令[tex=8.786x1.571]49UFtdxdDKQlKWZMhTPj6hyAgZG/3kqvw9AAiQjvsWfuDJ1TjZsW4IK5SRWqv9Pu[/tex]，得驻点[tex=5.214x1.357]XDrTulLJxux6t9cwxN1H0A==[/tex]以及[tex=1.786x1.214]LxzV0lHNWl1Oblvb2+onBQ==[/tex]的其他驻点。下面先对前两个驻点进行判定，由于[tex=14.786x5.214]rZM5/OPAdr7aX+kNl9iwpGTFVzcdQHZK/lXTMPqedf6re6GBq0GSeylBOu4g5qGKPSCzDvVuHlLiO+RUAgSG0RhtGE7X3a9CgHyB3wB3Ly1wozNhXP2uwixuNHjkXpynyBMekzaErc2GCcE2d7z6nZk9P4SV2Z0BVV3O9+8Ou5VtjxG6EW+xf7WY8kkMHjCFfAcqKveTWWA5WHz46epIsT74+HbIB4WTr+TsEm1V1NEPnEqrsechb/ZMbSxrgdvUmt3/AOTP3/G/rWte9IagU6tuAhVnJY2yHjXDpoLpmpZdhipfbWmR7mfk1bfk9IllGkSo2zOyVcYzbTnGDggvzDuOnpRyt+DtweK6YmI6y1o5tpjHVcOEaj7JikwnRFdnJa4O1yYApnsM90+VtasH2A==[/tex]而[tex=23.857x1.571]nc+aNBtr3itOBOADrUmiLhTE6HDEiCYebmyrsoCJ4ifzC6BFEXBsg/66Lax9QU+v/jqhyp/9pI5R0dQDj3H2p1wwdC+F658XA65w+l1HyNvc/MaDMTUUTps1jQUFX+oQJ1bCudeGyudULFgDhFDC8KxZNOld1BanXwa4emhgoQaIdH2WpPSSBMC4+nog4dmq[/tex]，故对于[tex=2.071x1.357]IVQHL7gpVvGMeTU2JgKtIg==[/tex]和[tex=3.0x1.357]JshCjEryEqDhTnmjRQ+7zg==[/tex]都有[tex=5.286x1.357]Mh084V0WFLVBeMb2t3xOGA==[/tex]，且[tex=2.643x1.071]LBILLgNuKcYFFr+o9ynKtg==[/tex]， 所以[tex=2.071x1.357]IVQHL7gpVvGMeTU2JgKtIg==[/tex]和[tex=3.0x1.357]JshCjEryEqDhTnmjRQ+7zg==[/tex]均为极大值点，且[tex=5.071x1.357]C8FE5T+CSC7el4cqHXUqCA==[/tex]。因为在边界[tex=3.857x1.429]wexgr6BjbEMq9oe2tZkPwJ1s/zN5XNiXXs0QkTiH7Cs=[/tex]上及[tex=1.786x1.214]LxzV0lHNWl1Oblvb2+onBQ==[/tex]的其他驻点处均有[tex=4.071x1.357]mv8GIdAUo0+16UAegEcsyw==[/tex]， 所以[tex=5.071x1.357]j/AzZjNclatmLv1QFL0Iqw==[/tex]为最大值。由上述讨论可知[tex=3.929x1.357]GEvB6NweW8cN38f69boCUREbsjh2pfdi7B0uMZi+v0c=[/tex]，即[tex=4.143x1.5]ibao9zGN1N3wbfx5dsehN50Lv/jtzLs3WMsewcG0wvgGKIpslfSzGDY4oLBTIt7/[/tex]。