解：设函数[tex=8.071x1.286]vsi9lTYW/Q9rlSkhQvPAw78or3KwJ+/kgHWvmrwRkgI=[/tex]。[tex=1.857x1.286]G6WxJ307HB2e1l7Qz3uNbQ==[/tex]在[tex=2.714x1.286]scYOl+SzOqdr9AOwlBxSjw==[/tex]上连续, 且 [tex=6.929x1.286]S1U6eOlcCwlkx3RvFdFndw==[/tex], [tex=5.429x1.286]0cYDk7GorYLWZFDdB5AK/g==[/tex] 。 由零点定理知至少存在一点[tex=4.571x1.286]U4fzRqb1a/ETt7oTNcfCG3JhwK3aB8k+vaXgfblglqI=[/tex]，使[tex=3.643x1.286]zlTa8MtwhCDPYWZctn92XQ==[/tex]即方程[tex=6.714x1.286]BqfAzYKNezdHxKAvdmh/Nua/2G46Js5J/qe+Sbbk3+A=[/tex]在区间[tex=2.929x1.286]3y4MkSHU4CkFowioH8YmWQ==[/tex]内至少有一实根。又[tex=8.429x1.286]nOJBJucVwlQuHq02hM9Tsli4g7P327gaM5hM9VSKYGY=[/tex]，故函数[tex=1.857x1.286]G6WxJ307HB2e1l7Qz3uNbQ==[/tex]在[tex=2.714x1.286]scYOl+SzOqdr9AOwlBxSjw==[/tex]上单调增加, 从而方程 [tex=3.714x1.286]0ZoDYEiHpPjb6Gw3Oeomrg==[/tex]即[tex=6.714x1.286]BqfAzYKNezdHxKAvdmh/Nua/2G46Js5J/qe+Sbbk3+A=[/tex]在[tex=2.929x1.286]3y4MkSHU4CkFowioH8YmWQ==[/tex]内至多有一个实根, 因此方程[tex=6.714x1.286]BqfAzYKNezdHxKAvdmh/Nua/2G46Js5J/qe+Sbbk3+A=[/tex] 在区间[tex=2.929x1.286]3y4MkSHU4CkFowioH8YmWQ==[/tex]内有惟一的实根。现用切线法求这个实根的近似值 :由 [tex=5.643x1.286]YRReUQzIsdcIgxj5peM19NWV+No5mhT+epqmJmBGW38OdA4kj7gkrPt7tKFRt92A[/tex], [tex=7.857x1.286]YRReUQzIsdcIgxj5peM19NhN1D/lHlLaKiSR8Y33o1DVVtveKBVvLM+McDcgXrjQ[/tex]知取[tex=3.5x1.286]fUwp9QkJKUEZuNpb7mEONA==[/tex]，利用递推公式[tex=5.214x1.286]2Jj9CSy8uBVaNuS36DTj9yWkz6b+y3bZtMS2ElfyET4=[/tex][tex=4.071x2.286]JqeIuNHU1e29UkfBBMnDaqYFaEaMh6Oc4Jjo7UAE6iSar4fUfh1YwUasT5b3rlixAgXaEy+n74n3uhwOFEjeV7hBIhlzhU9JJPHxqzQ4kSE=[/tex]，得:[tex=17.571x2.286]EnLWc5y2myTpndowtD1sju2tPfZ93NTdZUQ/B912XnNUoKPVeXOKtsJwnbKbFlh/nrYHcrWs5UOPhE0vJEz5Rd/4rOKlahxJ+FJhDDqo4U8SRSiUFkLQNjOTiEVGQxKqzHmb1BV26pQUysdSXB1Ddw==[/tex]，[tex=19.5x2.286]Z7vsslIDz1c4hEBweLGWf20P8miOEeAe0FKMFP2g7aToxdleobeWouV34LAAztJxxcGtsLeYfbviteI0ATRAcC1gp5aA+yGV1Jb9CPVFgshPNo5jmoLeunyCvS5NVOiXYgG6speYg9ce77HFdotirZFl8aX9ILJLD+sjV2Tq4Ao=[/tex]，[tex=20.5x2.286]t5S0Z4SZryYT4PzvQOiYEVtYjmX171yr9b+tU6ERZbcoY4FHpntPbW1jjigyREJlGxpm4pdurJtBwLdh4yYEqzIonyNJZJZlcSzCSheuvF/pA5wc+hqdl3LjQw1w9GJy/IEwFbEL/aFAFgo62jagzOk8Y1j/QiBTq5hSCSR5HnA=[/tex]，[tex=20.5x2.286]7xujd8FEK23eYVgY4NSfdLl5LTcnF9MExwEUb8G7ZkEJ1AmWzAk9ji27op51ryVhcsqeNjzpo4xfpK393yRGvdIdjwJtPNgc3vnbkHliDP5HopkemiO/RWm2QwawTJXKJ+h/uDPnyIKvRN0ZTN+Tc55zldEUzxJWxihh4RiRCTA=[/tex]。故使误差不超过 0.01 的根的近似值为[tex=4.286x1.286]kgQvruyEyBqLhPYucNE5tw==[/tex]。