ÌâÄ¿ÄÚÈÝ

¡¾ÌâÄ¿¡¿ÒÑÖªÅ×ÎïÏßy=-x2+bx+cµÄ¶¥µãPµÄ×ø±êΪ£¨n£¬n2+2n+1£©£¨n¡Ý1£©.

£¨1£©ÇóbÓën£¬cÓënÖ®¼äµÄ¹Øϵʽ£»

£¨2£©ÈôÅ×ÎïÏßy=-x2+bx+cÓëxÖá½»ÓÚµãA£¬B£¨µãAÔÚµãBµÄ×ó±ß£©£¬µãPµ½ABµÄ¾àÀëµÈÓÚÏ߶ÎAB³¤µÄ2±¶£¬Çó´ËÅ×ÎïÏßy=-x2+bx+cµÄ½âÎöʽ£»

£¨3£©ÉèÅ×ÎïÏßy=-x2+bx+cÓëyÖá½»ÓÚµãD£¬OΪԭµã£¬¾ØÐÎOEFDµÄ¶¥µãE£¬F·Ö±ðÔÚxÖáºÍ¸ÃÅ×ÎïÏßÉÏ£¬µ±¾ØÐÎOEFDµÄÃæ»ýΪ20ʱ£¬ÇóµãPµÄ×ø±ê.

¡¾´ð°¸¡¿£¨1£©b=2n,c=2n+1£»£¨2£©´ËÅ×ÎïÏßcµÄ½âÎöʽΪy=-x2+6x+7£»£¨3£©µãPµÄ×ø±êΪ£¨2£¬9£©.

¡¾½âÎö¡¿ÊÔÌâ·ÖÎö£º£¨1£©yPÓɶ¨µãPµÄ×ø±ê£¬¿ÉµÃÅ×ÎïÏߵĽâÎöʽΪy=-x2+2nx+2n+1=-x2+bx+c£¬×óÓÒ¶ÔÕÕ¼´¿ÉÇó³öbºÍc£»

£¨2£©¸ù¾ÝÅ×ÎïÏߵĽâÎöʽ¿ÉÇó³öAºÍBµÄ×ø±ê£¬ÓÖµãPµ½xÖáµÄ¾àÀëΪn2+2n+1£¬ËùÒÔÓÐn2+2n+1=2n+2£¬½â·½³ÌÇó³önµÄÖµ£¬½ø¶ø¿ÉÇó³öÅ×ÎïÏß½âÎöʽ£»

£¨3£©¸ù¾ÝÒÑÖªÌõ¼þ¿ÉÇó³öOD£¬DFµÄ³¤£¬ÔÙ¸ù¾Ý¾ØÐεÄÃæ»ý¹«Ê½¿ÉµÃ£ºODDF=2n£¨2n+1£©=20£¬Çó³önµÄÖµ£¬¼´¿ÉÇó³öPµÄ×ø±ê£®

ÊÔÌâ½âÎö£º£¨1£©¡ß¶¥µãPµÄ×ø±êΪ£¨n£¬n2+2n+1£©£¨n¡Ý1£©£¬

¡ày=-£¨x-n£©2+n2+2n+1=-x2+2nx+2n+1=-x2+bx+c£¬

¡àb=2n£¬c=2n+1£»

£¨2£©µ±y=0ʱ£¬¼´-x2+2nx+2n+1=0.½âµÃx1=-1£¬x2=2n+1.

ÓÉÓÚµãAÔÚµãBµÄ×ó±ß£¬

¡àµãAµÄ×ø±êΪ£¨-1£¬0£©£¬µãB µÄ×ø±êΪ£¨2n+1£¬0£©£¬

¼´AB=2n+1-£¨-1£©=2n+2£»

ÓÖµãPµ½xÖáµÄ¾àÀëΪn2+2n+1£¬

ÓÉÌâÒâ¿ÉµÃn2+2n+1=2n+2.½âµÃn=3£¬n=-1£¨²»ºÏÌâÒ⣬ÉáÈ¥£©£¬

¼´n=3£»

¡à´ËÅ×ÎïÏßcµÄ½âÎöʽΪy=-x2+6x+7£»

£¨3£©ÈçͼËùʾ£¬¡ßc=2n+1£¬

¡àµãDµÄ×ø±êΪ£¨0£¬2n+1£©£¬¼´OD=2n+1£¬

ÓÖ¡ßDF¡ÎxÖᣬÇÒD£¬F¹ØÓÚÖ±Ïßx=n¶Ô³Æ£¬

¡àFµÄ×ø±êΪ£¨2n£¬2n+1£©£¬

¡àDF=2n.

ÓÉÌâÒâ¿ÉµÃOD¡¤DF=20£¬¼´2n£¨2n+1£©=20£¬

½âµÃn=2»òn=-2.5£¨²»ºÏÌâÒ⣬ÉáÈ¥£©£¬¼´n=2£»

¡àµãPµÄ×ø±êΪ£¨2£¬9£©.

Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿

Î¥·¨ºÍ²»Á¼ÐÅÏ¢¾Ù±¨µç»°£º027-86699610 ¾Ù±¨ÓÊÏ䣺58377363@163.com

¾«Ó¢¼Ò½ÌÍø