ÌâÄ¿ÄÚÈÝ
1909Ä꣬Ħ¶û¸ù¿ªÕ¹Á˹ØÓÚ¹ûÓ¬°×ÑÛÐÔ×´ÒÅ´«µÄÑо¿£®Ëû½«°×ÑÛÐÛÓ¬Óë´¿ºÏµÄºìÑÛ´ÆÓ¬ÔÓ½»£¬F1´ú¶¼ÊǺìÑÛ£»F2´úÖУ¬ºìÑ۴ƹûÓ¬2459Ö»£¬ºìÑÛÐÛ¹ûÓ¬1011Ö»£¬°×ÑÛÐÛ¹ûÓ¬782Ö»£®£¨ÉèÓйػùÒòÓÃR¡¢r±íʾ£©
£¨1£©ÔÚÉÏÊö¹ûÓ¬ÑÛÉ«ÖУ¬ ÊÇÏÔÐÔÐÔ×´£¬ÆäÒÅ´«·ûºÏ ¶¨ÂÉ£®
£¨2£©Ò»¸ö´¦ÓÚÆ½ºâ״̬µÄ¹ûӬȺÌåÖÐr»ùÒòµÄƵÂÊΪa£®Èç¹ûÈ¡F2µÄÒ»Ö»°×ÑÛÐÛ¹ûÓ¬ÓëÒ»Ö»Õý³£µÄºìÑÛ´ÆÓ¬ÔÓ½»£®Ôòºó´úÖа×ÑÛ´ÆÓ¬µÄ¸ÅÂÊΪ £®
£¨3£©Ä¦¶û¸ùµÄѧÉú²¼ÀïÆæË¹ÔÚÖØ¸´Ä¦¶û¸ùµÄ¹ûÓ¬°éÐÔÒÅ´«ÊµÑéʱ£¬ÓÖ·¢ÏÖÁËÀýÍâÏÖÏó£®Ëû¹Û²ìÁË´óÁ¿µÄ°×ÑÛ´ÆÓ¬ÓëºìÑÛÐÛÓ¬µÄÔÓ½»ºó´ú£¬·¢ÏÖ´óԼÿ2000¸ö×Ó´ú¸öÌåÖУ¬ÓÐÒ»¸ö¿ÉÓýµÄ°×ÑÛ´ÆÓ¬»ò²»ÓýµÄºìÑÛÐÛÓ¬£®ÒÑÖª¼¸ÖÖÐÔȾɫÌåÒì³£¹ûÓ¬µÄÐÔ±ð¡¢ÓýÐÔµÈÈç±íËùʾ£®
²¼ÀïÆæË¹ÔÚ·ÖÎöÕâЩÀýÍâÏÖÏóµÄ²úÉúÊÇÓÉÓÚXȾɫÌåÔÚ £¨Ìî¾ßÌåʱÆÚ£©²»·Ö¿ªÔì³ÉµÄ£¬²úÉúÁË µÄÂÑϸ°û£®¾Ý´Ë·ÖÎö£¬ÇëÍÆ²âÀýÍâµÄ¿ÉÓý°×ÑÛ´ÆÓ¬×î¶àÄܲúÉú µÄÂÑϸ°û£®
£¨4£©ÒÑÖªÀýÍâµÄ°×ÑÛ´ÆÓ¬ÔÚ½øÐмõÊý·ÖÁÑʱ£¬Í¨³£ÊÇÁ½ÌõXȾɫÌåÅä¶Ô£¬¶øYȾɫÌåÓÎÀ룮¾Ý´Ëд³öÕâÖÖ°×ÑÛ´ÆÓ¬ÓëÕý³£ºìÑÛÐÛÓ¬ÔÓ½»µÄÒÅ´«Í¼½â£¬²¢ÓÃÊʵ±µÄÎÄ×Ö¸øÓè˵Ã÷£®
£¨1£©ÔÚÉÏÊö¹ûÓ¬ÑÛÉ«ÖУ¬
£¨2£©Ò»¸ö´¦ÓÚÆ½ºâ״̬µÄ¹ûӬȺÌåÖÐr»ùÒòµÄƵÂÊΪa£®Èç¹ûÈ¡F2µÄÒ»Ö»°×ÑÛÐÛ¹ûÓ¬ÓëÒ»Ö»Õý³£µÄºìÑÛ´ÆÓ¬ÔÓ½»£®Ôòºó´úÖа×ÑÛ´ÆÓ¬µÄ¸ÅÂÊΪ
£¨3£©Ä¦¶û¸ùµÄѧÉú²¼ÀïÆæË¹ÔÚÖØ¸´Ä¦¶û¸ùµÄ¹ûÓ¬°éÐÔÒÅ´«ÊµÑéʱ£¬ÓÖ·¢ÏÖÁËÀýÍâÏÖÏó£®Ëû¹Û²ìÁË´óÁ¿µÄ°×ÑÛ´ÆÓ¬ÓëºìÑÛÐÛÓ¬µÄÔÓ½»ºó´ú£¬·¢ÏÖ´óԼÿ2000¸ö×Ó´ú¸öÌåÖУ¬ÓÐÒ»¸ö¿ÉÓýµÄ°×ÑÛ´ÆÓ¬»ò²»ÓýµÄºìÑÛÐÛÓ¬£®ÒÑÖª¼¸ÖÖÐÔȾɫÌåÒì³£¹ûÓ¬µÄÐÔ±ð¡¢ÓýÐÔµÈÈç±íËùʾ£®
| ȾɫÌå×é³É | XXY | XO | YO | XYY | XXX |
| ÐÎ×´ | ´ÆÐÔ£¬¿ÉÓý | ÐÛÐÔ£¬²»Óý | ËÀÍö | ÐÛÐÔ£¬¿ÉÓý | ËÀÍö |
£¨4£©ÒÑÖªÀýÍâµÄ°×ÑÛ´ÆÓ¬ÔÚ½øÐмõÊý·ÖÁÑʱ£¬Í¨³£ÊÇÁ½ÌõXȾɫÌåÅä¶Ô£¬¶øYȾɫÌåÓÎÀ룮¾Ý´Ëд³öÕâÖÖ°×ÑÛ´ÆÓ¬ÓëÕý³£ºìÑÛÐÛÓ¬ÔÓ½»µÄÒÅ´«Í¼½â£¬²¢ÓÃÊʵ±µÄÎÄ×Ö¸øÓè˵Ã÷£®
¿¼µã£º»ùÒòµÄ·ÖÀë¹æÂɵÄʵÖʼ°Ó¦ÓÃ,°éÐÔÒÅ´«
רÌ⣺
·ÖÎö£º¸ù¾Ý°×ÑÛÐÛÓ¬Óë´¿ºÏµÄºìÑÛ´ÆÓ¬ÔÓ½»£¬F1´ú¶¼ÊǺìÑÛ»òF1´ú¶¼ÊǺìÑÛ£»F2´úÖУ¬³öÏÖºìÑۺͰ×ÑÛ£¬¶¼¿ÉÅжϺìÑÛ¶Ô°×ÑÛÏÔÐÔ£®Ã÷ȷ֪ʶµã£¬ÊáÀíÏà¹ØµÄ»ù´¡ÖªÊ¶£¬·ÖÎöͼ±í£¬½áºÏÎÊÌâµÄ¾ßÌåÌáʾ×ÛºÏ×÷´ð£®
½â´ð£º
½â£º£¨1£©½«°×ÑÛÐÛÓ¬Óë´¿ºÏµÄºìÑÛ´ÆÓ¬ÔÓ½»£¬F1´ú¶¼ÊǺìÑÛ£¬ËµÃ÷ºìÑÛΪÏÔÐÔÐÔ×´£»¸ù¾ÝÌâÒâ¿ÉÅжϺìÑۺͰ×ÑÛ»ùÒòλÓÚXȾɫÌåÉÏ£¬Òò´ËÑÛÉ«µÄÒÅ´«·ûºÏ»ùÒò·ÖÀ붨ÂÉ£®
£¨2£©¸ù¾ÝÒÅ´«Æ½ºâ£¬XrÊÇa£¬ËùÒÔXRÊÇ1-a£¬´Æ¹ûÓ¬ÖÐXRXRÊÇ£¨1-a£©2£¬XRXrÊÇ2a£¨1-a£©£¬ËùÒÔÕý³£µÄºìÑÛ´ÆÓ¬ÖÐXRXrËùÕ¼µÄ±ÈÀý
£¬Á½ÕßÔÓ½»ºó´ú°×ÑÛ´ÆÓ¬µÄ¸ÅÂÊΪ
£®
£¨3£©ÀýÍâÏÖÏóµÄ²úÉúÊÇÓÉÓÚÔÚ¼õÊýµÚ¶þ´Î·ÖÁѺóÆÚXȾɫÌåµÄ½ãÃÃȾɫµ¥Ìå·ÖÀëºó£¬·Öµ½Í¬Ò»¸öϸ°ûÄÚÔì³ÉµÄ£¬Òò´Ë²úÉúÁËXX»ò0µÄÂÑϸ°û£®°×Ñ۴ƹûÓ¬£¨XrXrY£©µÄÂÑÔϸ°ûÔÚ½øÐмõÊý·ÖÁѲúÉúÅä×ӵĹý³ÌÖУ¬ÓÉÓÚÐÔȾɫÌåÓÐÈýÌõ£¬ËùÒÔ»á³öÏÖÁª»áÎÉÂÒÏÖÏó£¬ÕâÑù×î¶à¿ÉÐγÉXr¡¢XrXr¡¢XrY¡¢YËÄÖÖÅä×Ó£®
£¨4£©ÓÉÌâÒâ¿ÉÖª£¬°×Ñ۴ƹûÓ¬£¨XrXrY£©ÄܲúÉúXr¡¢XrYµÄÅä×Ó£¬ÓëºìÑÛÐÛ¹ûÓ¬ÔÓ½»ºóÄܲúÉú±íÏÖÐͲ»Í¬µÄËÄÖÖºó´ú£®
¹Ê´ð°¸Îª£º
£¨1£©ºìÑÛ »ùÒò·ÖÀë
£¨2£©a/[2£¨a+1£©]
£¨3£©¼õÊýµÚ¶þ´Î·ÖÁѺóÆÚ XX»ò0 Xr£¬XrXr£¬XrY£¬Y
£¨4£©°×ÑÛ´ÆÓ¬ÓëÕý³£ºìÑÛÐÛÓ¬ÔÓ½»µÄÒÅ´«Í¼½â£º
£¨2£©¸ù¾ÝÒÅ´«Æ½ºâ£¬XrÊÇa£¬ËùÒÔXRÊÇ1-a£¬´Æ¹ûÓ¬ÖÐXRXRÊÇ£¨1-a£©2£¬XRXrÊÇ2a£¨1-a£©£¬ËùÒÔÕý³£µÄºìÑÛ´ÆÓ¬ÖÐXRXrËùÕ¼µÄ±ÈÀý
| 2a |
| 1+a |
| a |
| 2(a+1) |
£¨3£©ÀýÍâÏÖÏóµÄ²úÉúÊÇÓÉÓÚÔÚ¼õÊýµÚ¶þ´Î·ÖÁѺóÆÚXȾɫÌåµÄ½ãÃÃȾɫµ¥Ìå·ÖÀëºó£¬·Öµ½Í¬Ò»¸öϸ°ûÄÚÔì³ÉµÄ£¬Òò´Ë²úÉúÁËXX»ò0µÄÂÑϸ°û£®°×Ñ۴ƹûÓ¬£¨XrXrY£©µÄÂÑÔϸ°ûÔÚ½øÐмõÊý·ÖÁѲúÉúÅä×ӵĹý³ÌÖУ¬ÓÉÓÚÐÔȾɫÌåÓÐÈýÌõ£¬ËùÒÔ»á³öÏÖÁª»áÎÉÂÒÏÖÏó£¬ÕâÑù×î¶à¿ÉÐγÉXr¡¢XrXr¡¢XrY¡¢YËÄÖÖÅä×Ó£®
£¨4£©ÓÉÌâÒâ¿ÉÖª£¬°×Ñ۴ƹûÓ¬£¨XrXrY£©ÄܲúÉúXr¡¢XrYµÄÅä×Ó£¬ÓëºìÑÛÐÛ¹ûÓ¬ÔÓ½»ºóÄܲúÉú±íÏÖÐͲ»Í¬µÄËÄÖÖºó´ú£®
¹Ê´ð°¸Îª£º
£¨1£©ºìÑÛ »ùÒò·ÖÀë
£¨2£©a/[2£¨a+1£©]
£¨3£©¼õÊýµÚ¶þ´Î·ÖÁѺóÆÚ XX»ò0 Xr£¬XrXr£¬XrY£¬Y
£¨4£©°×ÑÛ´ÆÓ¬ÓëÕý³£ºìÑÛÐÛÓ¬ÔÓ½»µÄÒÅ´«Í¼½â£º
µãÆÀ£º±¾Ì⿼²é»ùÒò·ÖÀ붨ÂɺͰéÐÔÒÅ´«µÄÏà¹ØÖªÊ¶£¬ÒâÔÚ¿¼²éѧÉúµÄʶ¼ÇÄÜÁ¦ºÍÅжÏÄÜÁ¦£¬ÔËÓÃËùѧ֪ʶ×ۺϷÖÎöÎÊÌâµÄÄÜÁ¦£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿
ÏÂÁйØÓÚÖ²Îï¼¤ËØµ÷½ÚµÄÐðÊö£¬ÕýÈ·µÄÊÇ£¨¡¡¡¡£©
| A¡¢Ò»ÖÖ¼¤Ëصı仯¶¼½«ÒýÆðÆäËû¼¤Ëصı仯 |
| B¡¢ÒÒϩֻÔÚ¹ûʵÖкϳɣ¬²¢ÄÜ´Ù½ø¹ûʵ³ÉÊì |
| C¡¢Ö²Îï¼¤ËØÖ»ÄÜͨ¹ýÖ²ÎïºÏ³É |
| D¡¢ÔÚÖ²ÎïÌåÄÚ£¬Éú³¤ËØÖ»ÄܽøÐм«ÐÔÔËÊä |
| A¡¢ÔÚͬµÈÌõ¼þÏ£¬C4Ö²ÎïµÄa¿ÉÄÜÏò×óÒÆ |
| B¡¢ÇúÏß±íÃ÷£¬Ö²ÎïµÄ¹âºÏ×÷ÓÃÆðʼÓÚaµã |
| C¡¢ÔÓ½»ÓñÃ×µÄmÖµÍùÍù¸ßÓÚÒ»°ãÓñÃׯ·ÖÖ |
| D¡¢ÈôÅàÓý³öa¡«b¼ä¾à´óµÄÆ·ÖÖ£¬mÖµÓÐÍûÌá¸ß |