解由[tex=3.357x1.143]ikN/hcxoQ2qRIbjimrl9Lw==[/tex] 及[tex=1.857x1.0]kCYiW6QQC0U5Hqfo1w5wHA==[/tex]的图像知方程有正根,且有无穷个,只求其最小三正根,设[tex=6.786x1.357]BE6ixq5E1J00XEnXQsVCyw==[/tex](1)由于[tex=25.714x2.786]SYbizuqS4O0eHpNQ0pIL1SKISI0q2SotgVfXtm92lAAESWwiRBLc6Mrl1TUlo1lFaa+heSHQgxeO/JqHn1Y3G0SqyEKBFT61F+TVFCfo2qT3vEkeF4MawLVzK7rLKnX4cTYG1Iv9lhk88i7Ld0UMld5cZV3NFqp/N/55vi/HLyQ=[/tex]及[tex=9.429x2.786]EZx7/RUGilGAkrXSfDFFCwHMDTcuTLzVtvF27n5FjERYC9lr03cZOJr5RLxRdQN9ge0ZROQW/sCLLn4wNBt45A==[/tex],故在[tex=5.357x2.786]KZ5wO9ByCbKdJwoD25qQxPIexoG3tBLL/4imHX5KWLGigxsp0XxHuWWfoJIfNz0r[/tex]内所给方程有且仅有一实根[tex=0.857x1.214]94khMJrsXRzT+t74Gj49MQ==[/tex],切点应选在[tex=4.286x1.357]DS/vRLjJpujXTkWYi6eGeg==[/tex]处.依次求得[tex=0.857x1.214]94khMJrsXRzT+t74Gj49MQ==[/tex]的第[tex=0.357x1.0]+eJLelx8thmbkEj/Y0iCOw==[/tex]个近似值[tex=0.857x1.0]0xLUuCFuvbHeMBoeDGA2cg==[/tex]为:[tex=10.571x1.214]nhtQc5vHjSSZZGsQFBpirTQz1mBQdjFJyw7zm4y3QjjiqNbuOrpER4kQzrT90ZVo[/tex]由于[tex=22.357x2.786]HyPew8nKLElbl7w1hdVGZvvQzNYR3cUnUL8gWfDGB9fRjPkFkkBEz92BLo6KuEgJMSFf5Ef5wqMAxvTAzXS2mJMUgpoKUkxDbi3sm618N1+X1Y7IhdjshuYPgxqEy0hroTHO838pXw7xkIyfm6GU6GZjSzs1E8CTbLuwsjhosZw=[/tex] 因此,如果取4.493作为根[tex=0.857x1.214]94khMJrsXRzT+t74Gj49MQ==[/tex]的近似值,则其误差为[tex=13.286x2.429]TNCRxw1agch+Dtf9Ykl5DAYaeQ/2riupQqK/Tdwu+aSCMYKy6ilZJUqvpXVScD5jHDxkjiLvWg1UqYzQ7q9bCiO3wLEkHMLT6T9EqoDZGww=[/tex]已达到所需的精确度.于是,所给方程的一最小正近似根为4.493.(2)再求第二个最小正根.由于[tex=12.286x2.786]+x62DlQ9og1oQx3rhaiBsrFnRpsZjMGJ7z8TzlNW0JvPlHNnEKs9aWZ3ZMqXk7HNV7oTBxC3wuXgXi/RV/MqA+3ZmN5QnCq3LZ7uB1Zakpo=[/tex]故在[tex=5.857x2.786]leQybowFwTIJnXdLp55RxgiIotOzO+5N51uFT6wAqyD+oP3CZ6aHvQXyu06Qv1om8HmJ6KTG5pPfkmw3M/cS2A==[/tex]内方程有且仅有一实根[tex=0.857x1.214]yPVzDAW2UgMuepN4MkwdDw==[/tex].又因在此区间内[tex=9.0x1.429]3x4YIN5MvQuXqNEnNygCPzsFPfVVb6ENwB1FdWtEYGY=[/tex]故切点应选在[tex=7.857x2.786]22ay5ibInapsTa5bcYxpoVVL+zZKloRrQBxMEITik8de5fCA3pwyrMH5lv/a2YJdji6w7IIc7A+m+AuIv8ul7joVnS+DbU0p5P2BKRfZNA4=[/tex]处.依次求得[tex=0.857x1.214]yPVzDAW2UgMuepN4MkwdDw==[/tex]的第[tex=0.357x1.0]+eJLelx8thmbkEj/Y0iCOw==[/tex]个近似值[tex=0.857x1.0]0xLUuCFuvbHeMBoeDGA2cg==[/tex];为:[tex=16.286x1.214]gRkAJgyRK42UbR4d5szvtP1BuhNkpDQLsHkMFfb1Fgn76rxEi82zWLy627Tq3duu4Zg1Fgmu+m15mlKP1QHYyQ==[/tex]由于[tex=24.0x2.786]bUe2gvJ+pPsjig+2YheebiJj9BTa0PTbXgjKvDI3jNQeRWi8f1Li+SojwAnuIn2WhltbnX4h4CfkLt92+W8ZgZ/Lu1vajnrZJBSbwdEEUszpY0oxemQyKzBrFAYLxtTFvK+4qrmZMwHrH65UGjQ+Hr8m04x361wO1QhKZ/rsee4=[/tex]因此,如果取7. 725作为[tex=0.857x1.214]yPVzDAW2UgMuepN4MkwdDw==[/tex]的近似值,则其误差为[tex=13.286x2.429]q4Rf0NPCApldTZ8TzDhL37GE7nLu9Mdn9a99RyCHkCnzxs8+8igTAL162q9x7aFZavkxKKY4zhd2du1e9CRcWd+QcZe0ZkKxY4aHgAE3fFQ=[/tex]巳达到所需的精确度.于是,所给方程的第二个最小正根的近似值为7.725.(3)最后求第三个最小正根.由于[tex=13.286x2.786]e+csrDmO7LAvIt5axdlXFjYOLtoTuh5pLbjju9W2cl0mNBSFGlLwgb0ahFWonyzNDgvHO9FRLiCUmxpmiQkXM8X89xoeykSMxorGWdOgqwA=[/tex]故在[tex=6.857x2.786]6l+G7QPbzOHcZ9Ly+Zus5QhIN81I9JTLiu63t4n3bO38ANoVQzapOXq2AFYg1udGvN2TMP27Ce9o5nuBF25Khw==[/tex]内方程有且仅有一-实根6.又因在此区间内[tex=9.0x1.429]3x4YIN5MvQuXqNEnNygCPzsFPfVVb6ENwB1FdWtEYGY=[/tex]故切点应选在[tex=8.857x2.786]TJrcfKxqdPXCdFii0Aif9JShqlWVHnRJOGqG2q/scjXyR3m+qxhF61fFwPGYpUdhH4TFc8WKrg4gvxDbA67AGlQlQ8Bt1QmQraBcSBoW+sE=[/tex]处.依次求得与的第[tex=0.357x1.0]+eJLelx8thmbkEj/Y0iCOw==[/tex]个近似值[tex=0.857x1.0]0xLUuCFuvbHeMBoeDGA2cg==[/tex]为:[tex=17.786x1.214]S+UIk++DPLVVA07nISh+sRqDqc0297FpelkV14Hj6BGpXJdcrup+0M+7VvI+/MXxMdhMbeIofjBsvoAkEZw3eA==[/tex]由于[tex=18.5x2.357]2Hyi5MUUicIiK9/n22ygtZamp2nZ+aPalrOT6vrrrC2U86aZk+Gys0hSFLzKaEs7MZGzJz6DF1MEB66MMDSR8Q==[/tex]因此,如果取10.904作为5s的近似值,则其误差为[tex=13.786x2.429]q4Rf0NPCApldTZ8TzDhL3xeF3CLKSeLWNneOUUS4zVRWb7yukGzM0bLFIEQRna8aRQq/2Fk4GOiy5sMj981oaTVnEp4ZxttkXLSkTDvDzDM=[/tex]已达到所需的精确度.于是,所给方程的第三个最小正根的近似值为10.904.