ÌâÄ¿ÄÚÈÝ

11£®ÒÑÖªº¯Êýf£¨x£©=$\left\{\begin{array}{l}{-{x}^{2}+4x-3£¬1¡Üx¡Ü3}\\{x-3£¬x£¾3}\\{\;}\end{array}\right.$£¬ÈôÔÚÆä¶¨ÒåÓòÄÚ´æÔÚn£¨n¡Ý2£¬n¡ÊN*£©¸ö²»Í¬µÄÊýx1£¬x2£¬¡­£¬xn£¬Ê¹µÃ$\frac{f£¨{x}_{1}£©}{{x}_{1}}$=$\frac{f£¨{x}_{2}£©}{{x}_{2}}$=¡­=$\frac{f£¨{x}_{n}£©}{{x}_{n}}$£¬ÔònµÄ×î´óÖµÊÇ3£»Èôn=2£¬Ôò$\frac{f£¨{x}_{n}£©}{{x}_{n}}$µÄ×î´óÖµµÈÓÚ4-$2\sqrt{3}$£®

·ÖÎö ×÷³öf£¨x£©µÄͼÏó£¬ÀûÓÃ$\frac{f£¨{x}_{1}£©}{{x}_{1}}$=$\frac{f£¨{x}_{2}£©}{{x}_{2}}$=¡­=$\frac{f£¨{x}_{n}£©}{{x}_{n}}$=kµÄ¼¸ºÎÒâÒåÊǹýÔ­µãµÄÖ±ÏßÓëf£¨x£©ÏཻµãµÄбÂÊ£®ÀûÓÃÊýÐνáºÏ½øÐÐÇó½â¼´¿É£®

½â´ð ½â£º×÷³öº¯Êýf£¨x£©µÄͼÏóÈçͼ£º$\frac{f£¨{x}_{1}£©}{{x}_{1}}$=$\frac{f£¨{x}_{2}£©}{{x}_{2}}$=¡­=$\frac{f£¨{x}_{n}£©}{{x}_{n}}$=kµÄ¼¸ºÎÒâÒåÊǹýÔ­µãµÄÖ±ÏßÓëf£¨x£©ÏཻµãµÄбÂÊ£¬
ÓÉͼÏóÖª¹ýÔ­µãµÄÖ±ÏߺÍf£¨x£©×î¶àÓÐ3¸ö½»µã£¬¼´nµÄ×î´óÖµÊÇ3£¬
Èôn=2£¬ÔòÖ±ÏßÓëf£¨x£©ÓÐÁ½¸ö½»µã£¬
Ôòµ±¹ýÔ­µãµÄÖ±Ïßy=kxµÄбÂÊk=0£¬»òÕßy=kxÓëf£¨x£©ÔÚ1¡Üx¡Ü3ÏàÇÐʱµÄбÂÊ£¬
ÆäÖÐ$\frac{f£¨{x}_{n}£©}{{x}_{n}}$µÄ×î´óֵΪy=kxf£¨x£©ÔÚ1¡Üx¡Ü3ÏàÇÐʱµÄбÂÊ£¬
½«y=kx´úÈëy=-x2+4x-3£¬µÃkx=-x2+4x-3£¬¼´x2+£¨k-4£©x+3=0£¬
ÓÉÅбðʽ¡÷=£¨k-4£©2-12=0µÃk-4=¡À$2\sqrt{3}$£¬¼´k=4¡À$2\sqrt{3}$£¬
¡ß·½³ÌµÄ¸ùx=$-\frac{k-4}{2}$¡Ê£¨1£¬2£©£¬
¡à0£¼k£¼2£¬Ôòk=4-$2\sqrt{3}$£¬
¹Ê$\frac{f£¨{x}_{n}£©}{{x}_{n}}$µÄ×î´óÖµµÈÓÚ4-$2\sqrt{3}$£¬
¹Ê´ð°¸Îª£º3£¬4-$2\sqrt{3}$

µãÆÀ ±¾ÌâÖ÷Òª¿¼²é·Ö¶Îº¯ÊýµÄÓ¦Óã¬ÕýÈ·Àí½â$\frac{f£¨{x}_{1}£©}{{x}_{1}}$=$\frac{f£¨{x}_{2}£©}{{x}_{2}}$=¡­=$\frac{f£¨{x}_{n}£©}{{x}_{n}}$=kµÄ¼¸ºÎÒâÒåÊǹýÔ­µãµÄÖ±ÏßÓëf£¨x£©ÏཻµãµÄбÂÊ£¬Êǽâ¾ö±¾ÌâµÄ¹Ø¼ü£®×¢ÒâÀûÓÃÊýÐνáºÏ½øÐÐÇó½â£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿

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

¾«Ó¢¼Ò½ÌÍø