设[tex=1.429x1.214]rkgrF+YaaESwSQDjR6KfWg==[/tex]是整数,证明[tex=4.857x1.5]9duS+gm+2rb/tFhqcKHb6z02OO2l+OBcJFVrh71rbro=[/tex]当且仅当 [tex=1.857x1.357]R7P3rDqk4IKKJcMYA7eBhg==[/tex]且 [tex=2.0x1.357]X7KCgVrOMpOqaVVLyt3Rlg==[/tex]

2022-05-29

设[tex=1.429x1.214]rkgrF+YaaESwSQDjR6KfWg==[/tex]是整数,证明[tex=4.857x1.5]9duS+gm+2rb/tFhqcKHb6z02OO2l+OBcJFVrh71rbro=[/tex]当且仅当 [tex=1.857x1.357]R7P3rDqk4IKKJcMYA7eBhg==[/tex]且 [tex=2.0x1.357]X7KCgVrOMpOqaVVLyt3Rlg==[/tex]

答案：

充分性显然. 必要性.[tex=33.929x1.286]QAGJrb4grkAR6hxtkyLM6wIGndU7D3stkB3RcdPHICmPPsLm18kZ874ajsSH5TpJa5F1hEe8zMYJVLtBwz3nj2C51rpZ69IJrrW5cs2TLfkzTp00lzwuPrP16+A+LlEqMjQ/xCWEBIjYdOzIVqFvmqENVwTo7dnLPMotBF5hO0KR9JVJuP+qItXrqm/F/N1yXtnePZsEBkHXEl6ZU06+ww==[/tex],[tex=19.143x1.286]EEjsTODYahwtIOPBnH85DoNf9fbVe2V1xS23lVrsUZoxVH2/Rk0eoalHAfTGoANsd9PsD81XmGxNwHO8nGptYypxC9pki4qdGCN7pzWGZ1atbLRoPi6QiBAnAWdIXrCB[/tex]而[tex=23.714x1.286]bYwi0U8ipWsu2PsH1oBUAEKUlfd8OpU92ZI0c1rlOMUjaivqV6Xvt5+gBeNif2t+UeuBd4Htznco4qRnPhYZzl20WsLSZUyt5BuubwY087gtsoLFkswuNY0BpBZrNOvt[/tex]不难验证: 只有当 [tex=9.0x1.286]CnVmNoFzenJxGK25RIAWgkiRyU4i1aMKU+BKEjGcoPCdzo2EweyEyCiY+Kn51pk7[/tex] 时,才有[tex=8.929x1.286]MgfBZj87DC0iMLbz4Xs88VWHL/Fh4xG1htwd1E9Q/dSFYSQFiLzZ7q0N+ULrKAUk[/tex].得证[tex=7.786x1.357]f/hrJ7FPKjVXQakS2TW//ZrBYY2WOSNqhEeWNdZLiiY4wEPZzHMvvcSryYTG1uIm[/tex].

举一反三

内容

0
设 [tex=5.571x1.214]eJy7VhH65VRts6bfN/wW0qSLr6tx3UnjbIVZOYmgwsesZVe3LfON1m5XC/ZWRrMkgjy0XGvwUDiz8worWVhiiA==[/tex] 且 [tex=6.0x1.429]VfJMl/JRDhUg4N/j0auYnx91sJmE1DpqMHmFSN4UNcv1AaUPUDKP71ackj4WfGz6cmsXyPO/7LbhB5qW3HMOIQ==[/tex] 证明1) [tex=5.0x1.357]PF4+0fQrOtrBMOGLTbiojWHD9HeQmUzzlH8ydOx6ZwA=[/tex] 当且仅当 [tex=6.714x1.214]t4fgzvN247twKwYp+jekqaSM2F1I59tfyLmarSTXF4jE9lVv1R3jnvrDqwnb09fgUQmV/i9jvGb1VP+NNe+qqJa017u08tzfXp2iJTfc89g=[/tex]2) [tex=5.429x1.0]bm3Mth7dIBkvW5h/YcCTdo75g2LQal/3MslYLuzIX7ljVLOMmokJVQ3pqIFz3ScpDLxYC3YRlx9OGboSSdFkPA==[/tex] 当且仅当 [tex=6.429x1.214]t4fgzvN247twKwYp+jekqd5tQX6Ir1tVtuMZ4EYdcuM175TWc9SLTF5enyW9KACLFLU5unY24y0o6hpa7IDat+mjWrcIYnd8nNNZzeFfjL8=[/tex].
1
设 [tex=4.0x1.214]gqm0mWUCKdOARf086AW0480jEQ3Xm81NfZLfINt8SrF3Bc8hkj34rbCcz4E0io/L[/tex] 试证1) [tex=2.571x1.143]WdbVvotJqaIEmmV0vNMW+jEQ83lsj5/Yim9TL3pJrZU=[/tex] 当且仅当 [tex=4.286x1.143]80Wj0uAKV+7pqHZEfv32mPI23ILOBLq3IKynnNCFOURqLDiirzP1JdUlbdFmI9kX[/tex], 且 [tex=0.786x1.0]PutU1cWdyHyySBp7YfCWhQ==[/tex] 的特征根都是实数;2) [tex=3.286x1.286]V5aIETDsYc6y76PNWXSA4NaDDrtbuCAhe1mIrkwO9SM=[/tex] 当且仅当 [tex=4.286x1.143]80Wj0uAKV+7pqHZEfv32mPI23ILOBLq3IKynnNCFOURqLDiirzP1JdUlbdFmI9kX[/tex], 且 [tex=0.786x1.0]PutU1cWdyHyySBp7YfCWhQ==[/tex] 的特征根都是纯虚数;3) [tex=3.5x1.214]kePI5SUwTOUcyZnmRV2Ep1OrfmgdKBaQ/84vMQv9BMA=[/tex] 当且仅当 [tex=4.286x1.143]80Wj0uAKV+7pqHZEfv32mPI23ILOBLq3IKynnNCFOURqLDiirzP1JdUlbdFmI9kX[/tex], 且 [tex=0.786x1.0]PutU1cWdyHyySBp7YfCWhQ==[/tex] 的特征根的模为 1 .
2
设[tex=5.929x1.071]gAFI4ZzNAmjFfJAphmTsRQ==[/tex]，若[tex=7.786x1.357]09fTpcwFMVcu1qrv9hyVbjaVP6Nu0Q7b0o9JCaEhfzk=[/tex]，[tex=7.786x1.357]17Fg+KbtgLZdNaerla1J+g==[/tex]，[tex=7.714x1.357]GzWWzGNDry0+/hdju2Gv5Q==[/tex]，那么[tex=0.571x0.786]/uIIzJZ/1DPgc5sOsRpAXQ==[/tex]，[tex=0.571x1.0]Tr41q2//n6lfFMLRmh8s0w==[/tex]，[tex=0.5x0.786]rGd4FFr4Zsu+cuz6gxITMA==[/tex]的大小关系为 A: x<y<Z B: y<z<x C: z<x<y D: z<y<x E: 不能确定
3
证明: 在 [tex=2.0x1.357]beH6DnGK6LEsYI2cIHxhuQ==[/tex] 中, [tex=5.429x1.5]0iDoJ5QK8zi3usxeb0s36HsBEi68g+g96husEUabpFA=[/tex] 当且仅当 [tex=4.786x1.357]U6R4KZ/ZA1xG3kNTBBaoT+B9yT2CBY1iERh1UZvi0XA=[/tex]
4
试证明下列命题：设 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 是 [tex=2.0x1.357]bXp5Vb63IyKXaWMS3BCP6w==[/tex] 上非负实值可测函数,则 [tex=2.357x1.5]TmZtGKi/BCqH3lxpzbIvTA==[/tex] 在[tex=2.0x1.357]bXp5Vb63IyKXaWMS3BCP6w==[/tex]上可积当且仅当[tex=15.571x3.286]eo4+Or2nRjPO1XMeI9CVMLCld2Jvji1B1hCYEjgm+3hZX53nHkOMnxdeFlHRDd5BqBiBcUx0hBMdjSd3+eraCJa4cwwxkYMiSX092RHmb4tgcpPJQ2+guLKcbAELFt0p[/tex].