Question

ÒÑÖªº¯Êý£¬·½³Ìf£¨x£©=-2x+7ÓÐÁ½¸ö¸ùx₁£¬x₂£¬ÇÒx₁£¼1£¼x₂£¼3£®
£¨1£©Çó×ÔÈ»ÊýaµÄÖµ¼°f£¨x£©µÄ½âÎöʽ£»
£¨2£©¼ÇµÈ²îÊýÁÐ{a_n}ºÍµÈ²îÊýÁÐ{b_n}µÄÇ°nÏîºÍ·Ö±ðΪS_nºÍT_n£¬ÇÒ£¬É裬Çóg£¨n£©µÄ½âÎöʽ¼°g£¨n£©µÄ×î´óÖµ£»
£¨3£©ÔÚ£¨2£©Ð¡ÌâµÄÌõ¼þÏ£¬Èôa₁=10£¬Ð´³öÊýÁÐ{a_n}ºÍ{b_n}µÄͨÏ²¢Ì½¾¿ÔÚÊýÁÐ{a_n}ºÍ{b_n}ÖÐÊÇ·ñ´æÔÚÏàµÈµÄÏÈôÓУ¬ÇóÕâЩÏàµÈÏî´ÓСµ½´óÅÅÁÐËù³ÉÊýÁÐ{c_n}µÄͨÏʽ£»ÈôûÓУ¬Çë˵Ã÷ÀíÓÉ£®

Answer 1

¡¾´ð°¸¡¿·ÖÎö£º£¨1£©ÓÉ·½³Ìf£¨x£©=-2x+76¿ÉÒÔ»¯¼òΪ£ºx²+£¨a²-23£©x+8=0£¬Áîh£¨x£©=6x²+£¨a²-23£©x+8£¬ÔÙ½áºÏ¶þ´Îº¯ÊýµÄÐÔÖʿɵÃa=2£¬½ø¶øÇó³öº¯ÊýµÄ½âÎöʽ£®
£¨2£©ÓɵȲîÊýÁеÄÐÔÖʿɵ㺣¬¼´¿ÉÇó³öº¯Êýg£¨n£©µÄ±í´ïʽ£¬½ø¶øÀûÓú¯ÊýµÄÓйØÐÔÖÊÇó³öÆä×î´óÖµ£®
£¨3£©£¬ÓÉ£¬ÔÙÀûÓã¨2£©ÖеĽâÎöʽÓëµÈ²îÊýÁеÄÐÔÖʿɵÃÁ½¸öÊýÁеÄͨÏʽ£¬½ø¶ø¼ÙÉè´æÔÚÏàµÈµÄÏîa_k=b_p£¬¿ÉµÃì¶Ü¼´¿ÉµÃµ½´ð°¸£®
½â´ð£º½â£º£¨1£©Óɵãº6x²+£¨a²-23£©x+8=0£»
Áîh£¨x£©=6x²+£¨a²-23£©x+8£¬ÓÉx₁£¼1£¼x₂£¼3µÃ£º£¬
ÓÖa¡ÊN£¬ËùÒÔÓУºa=2£»¡­£¨5·Ö£©
ËùÒÔ£» ¡­£¨6·Ö£©
£¨2£©£¬²¢ÇÒ½áºÏµÈ²îÊýÁеÄÐÔÖʿɵãº
£¬
ËùÒÔ£»¡­£¨8·Ö£©
²¢ÇÒ£®¡­£¨12·Ö£©
£¨3£©£¬ÓÉ£» ¡­£¨13·Ö£©
ÉèÊýÁÐ{a_n}ºÍÊýÁÐ{b_n}µÄ¹«²î·Ö±ðΪd₁£¬d₂£»
ËùÒÔ¡­£¨16·Ö£©
Èô´æÔÚÏàµÈµÄÏîa_k=b_p£¨k£¬p¡ÊN^*£©£¬¼´16k-6=12p-8⇒6p-8k=1¢Ù
¢Ùʽ×ó±ßΪżÊý£¬ÓÒ±ßΪÆæÊý£¬²»¿ÉÄܳÉÁ¢£¬
¹Ê²»´æÔÚÂú×ãÌõ¼þµÄÊýÁÐ{c_n}£®¡­£¨18·Ö£©
µãÆÀ£º±¾ÌâÖ÷Òª¿¼²é¶þ´Îº¯ÊýµÄÓйØÐÔÖÊÓëµÈ²îÊýÁеÄÓйØÐÔÖÊ£¬ÒÔ¼°µÈ²îÊýÁеÄͨÏʽ¡¢º¯ÊýÇó×îÖµµÈ֪ʶµã£®