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设平面上区域 [tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex] 在 [tex=0.571x1.286]XubEW9+1+hkJqH7jXe5MrA==[/tex] 轴和 [tex=0.571x1.286]Hz6y44ELFVLLNrLVhO3CQA==[/tex] 轴上的投影长度分别为 [tex=0.786x1.286]/iN9AKqTlzWqF66vwsFjlw==[/tex],[tex=0.714x1.286]vNO3e9/Alfn70oHKPnoPug==[/tex], [tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex] 的面积为 [tex=1.357x1.286]E2EhGPHm3hJLarmUkYwjfQ==[/tex], [tex=2.357x1.286]N+v3z11GnQYJh1AgKKnUSYpB5B68xiJf/p3QNHAAz8Q=[/tex] 为 [tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex] 从任一点,证明(1) [tex=7.0x2.214]RLkleDL+OME8UV5hgwTlCYP9imZagwxZ4SWNR0+U3LuTS18uMipPXrLSfoNUJXH2[/tex][tex=7.5x1.286]Tik/YnEVI0k3IYyWRjroXbksw5F3TxvTKZRvqqRHM8DlxtStHlBi807u47sar3+9[/tex];(2) [tex=7.0x2.214]lZgvkCxFYDJ6nFvKV+I/owJjsISSs0XxCaTaHEZ2Sxqjg6NUEUZwuBMUWQF++Ssf[/tex][tex=6.714x2.143]Tik/YnEVI0k3IYyWRjroXfehdUouAyLaazUeFFrstgBp1h+cvglwrFDVESoDHXYqB7Ai+bBeS0jCBTCFgWYUKRT/K+94e7mfpg3a8YpuHk4=[/tex].

设平面上区域 [tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex] 在 [tex=0.571x1.286]XubEW9+1+hkJqH7jXe5MrA==[/tex] 轴和 [tex=0.571x1.286]Hz6y44ELFVLLNrLVhO3CQA==[/tex] 轴上的投影长度分别为 [tex=0.786x1.286]/iN9AKqTlzWqF66vwsFjlw==[/tex],[tex=0.714x1.286]vNO3e9/Alfn70oHKPnoPug==[/tex], [tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex] 的面积为 [tex=1.357x1.286]E2EhGPHm3hJLarmUkYwjfQ==[/tex], [tex=2.357x1.286]N+v3z11GnQYJh1AgKKnUSYpB5B68xiJf/p3QNHAAz8Q=[/tex] 为 [tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex] 从任一点,证明(1) [tex=7.0x2.214]RLkleDL+OME8UV5hgwTlCYP9imZagwxZ4SWNR0+U3LuTS18uMipPXrLSfoNUJXH2[/tex][tex=7.5x1.286]Tik/YnEVI0k3IYyWRjroXbksw5F3TxvTKZRvqqRHM8DlxtStHlBi807u47sar3+9[/tex];(2) [tex=7.0x2.214]lZgvkCxFYDJ6nFvKV+I/owJjsISSs0XxCaTaHEZ2Sxqjg6NUEUZwuBMUWQF++Ssf[/tex][tex=6.714x2.143]Tik/YnEVI0k3IYyWRjroXfehdUouAyLaazUeFFrstgBp1h+cvglwrFDVESoDHXYqB7Ai+bBeS0jCBTCFgWYUKRT/K+94e7mfpg3a8YpuHk4=[/tex].

发布时间：2025-06-30 14:42:51

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答案：证: 设 [tex=0.857x1.286]s+r8LBAs3scxfl88DGExcg==[/tex] 里 [tex=0.571x1.286]XubEW9+1+hkJqH7jXe5MrA==[/tex] 轴和 [tex=0.571x1.286]Hz6y44ELFVLLNrLVhO3CQA==[/tex] 轴上的投影区间分别为 [tex=1.929x1.286]vPlUmwL8t1REs9r1XOy2kg==[/tex] 和 [tex=1.857x1.286]TaQDUPTPF82mJndYOqgzrA==[/tex]. 因此 [tex=4.214x1.286]MFylGl/fJcIE5qGkMfTiIA==[/tex], [tex=4.214x1.286]BZw8juJl11BVJ4/8vsJphA==[/tex], 并且[tex=4.929x1.286]7A46cC8EJnF4t7EMX3imxCA+ZEuP11n6oIKFX/iDeDQ=[/tex] , [tex=4.857x1.286]9agbql8CqhS/emCMx7XXe+eraF9Jau2NEXtm4hunqnzNEo58Qp0D0ZwRuIga8m/1[/tex],(1) [tex=10.571x4.0]FJGV9tkSDMyDUKglwq5q3Dfm8EIoaslrB7DsBQuAvMQo4Qbh5JjChYsfY5094sfp25KPkjKRBxNMqsjLKiC/4/0YWteT3rjql2iYLshWpQRqgv+v5xOlYbc8Iw8VmeP/[/tex][tex=9.643x3.357]h+Ma+TyC/ROodcIlT5RkdovKXZfWbArl16faXv8vLXjdQB/x9ogv7xyCES5etP271JdM3+7icX8x+rOULaFkTfrXG0lklVk7VlQQpJ9H1Rk=[/tex][tex=10.071x3.357]xi/C9IdUEd6LCnHqY3Ux9N5NiQ10cY/UPc97i8cdvBZiH7d6Z4TOmX3YjEuniWIB/mmTfkGMWkMPbJZRoWjazxVggMv9KC7MMe4Z92MBl/4bn/KI4DY+JLlWW59y28zg[/tex](2) [tex=10.429x4.0]FJGV9tkSDMyDUKglwq5q3Dfm8EIoaslrB7DsBQuAvMQ3ToGYz7E5STK/Jiw3U3jpzYHr/YmVhQi4tctvZwYBCf0b5qOKjzrdrYGqAEQyXHhp29DhT701a+ciC73uLvom[/tex][tex=11.643x2.5]hoIAqiFlhp8OrpL+oUbQDRBCX7O+TF1Vi90vm3hcjDYOLfRq8wi0l2n9oJf3Ff7gMmyxWWbqljj6yMoSYHfOMA==[/tex]考虑 [tex=5.5x2.5]hoIAqiFlhp8OrpL+oUbQDbPd63PwYR2OT2x7gRk72QU=[/tex] . 令 [tex=4.143x1.929]we8HiJ41odmi584b78pi1tH0Z/nqwPmiWt5NL+7gAlo=[/tex] [tex=4.643x1.286]JS3OVLy3Dls1T0Erh6r9SF4q7fASefzE9OxR4UMS11LcZdDtLUlsnVwb782eTTcA[/tex], 记 [tex=5.857x2.143]pxyomlSq0tiAUeDPGM1m1t8oAbx5f20eg3ivBLYRjidxUYjV7j8VniqIy6oDNcz9[/tex] [tex=4.786x1.286]XV+yIwWV8ny+jDnxcZ5GHP7JRqoYlXEyPsi3uG1dQJ+hknZzYkDtxIlFvtIVM/gE[/tex][tex=3.929x1.286]JnV7F6pcv5rs5hR893cOEHvmaWQ9WjpMACKucA5CkOw=[/tex][tex=7.357x1.286]u99KH91mwmGfrEXl9HIJr8zKjcHOwCK7NhSO4hS0h84=[/tex][tex=5.143x1.286]eavacei+TBWp7IV9zGrp9MpPc2BvdeA7e5lrK14odSlS5zlIuvwxr49gly06r72D[/tex][tex=3.357x1.286]BKBobFF0nZx884a06X13+/NWx1Q1wwJSSa+IdIcxC2E=[/tex][tex=6.5x2.5]hoIAqiFlhp8OrpL+oUbQDXuSWCpMi0CYjwvMYHVggtvQfkqipHTF7A+ge6qm1CFq[/tex][tex=7.143x2.5]YVkfRR/QZm5wGk+dYtrq2XuAK0oM/YywPSs+ya8C5EozIayQ7xUUm/k1ouZxcPO1[/tex][tex=7.0x2.429]vNJxz3JpJi4JBKbQGQRRKyb0ZbP5GLv4FcRmSLO1KkMqtRwdI2PlzK6tPorQMmTI[/tex][tex=6.786x2.286]vNJxz3JpJi4JBKbQGQRRKwikIlR3FxosCOxo9O6Lc6GrgO629aqh4aWo4n/e4R+7[/tex][tex=6.0x2.571]/gjzfXUHpNZ2zfFaofnLVgkol2CxufA30NLzHvRt7lMU6S/ce8ODB8rURq4YpRA+[/tex][tex=7.143x2.357]8+DQLqukWiJ1rg6DBgMZoS2bDzaCA3aBk8qMs5orFJJyNLnAr0/CA/afWd8NYGPtX/uWHFWIHCxzGXKxWTNXXA==[/tex]由于 [tex=4.071x1.286]DEduup92bkkF9RQZR20Aid2co8IEKWx/SE5umUzDCiLq4rnLi/RU6PPjNvUDMOXL[/tex], 因此 [tex=5.214x1.286]6ePdVXCMOzIHtAfLprAfFdyjJzR/Ow9rHTxsSJ3LNAA=[/tex]. 所以[tex=7.571x2.857]/5h+DKlZSLAPIP077AbnRUSlub5uUKDHiRefbf6NGuIW//74LTKVT+Qg3+IChj6MMb/fKL/yq19YVO9DIce7kQ==[/tex]同理可证 [tex=7.5x2.857]KU0emm9f9WmHV/ToQ52iYwck6AjE2Mwzdh0h80B5i/7yRjvdkwxV7i/r/RcPQqpI0aryXNYaWXb9K4APwovCqg==[/tex]得到 [tex=6.214x3.357]Uc5ox6CyWG8kmIHowYt3+6f865bvcmoyU1w05EnhAyuWq9T55GZW89x86pmrpfZO[/tex][tex=6.357x2.214]Tik/YnEVI0k3IYyWRjroXX4s1KpFRV4D2wsFjOqayWoh13YS1VlPAb3CDKjVdewBglMCUlzq0LDSGijyCMCWDg==[/tex].

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