Question

Èçͼ£¨1£©£¨2£©£¬Ö±Ïßy=-x+4ÓëÁ½×ø±êÖá·Ö±ðÏཻÓÚA¡¢Bµã£¬µãMÊÇÏ߶ÎABÉÏÈÎÒâÒ»µã£¨A¡¢BÁ½µã³ýÍ⣩£¬¹ýM·Ö±ð×÷MC¡ÍOAÓÚµãC£¬MD¡ÍOBÓÚD£®
£¨1£©ÈôµãMµÄºá×ø±êÊÇa£¬ÔòµãMµÄ×Ý×ø±êÊÇ

-a+4

£¨Óú¬aµÄ´úÊýʽ±íʾ£©
£¨2£©µ±µãMÔÚABÉÏÔ˶¯Ê±£¬ÄãÈÏΪËıßÐÎOCMDµÄÖܳ¤ÊÇ·ñ·¢Éú±ä»¯£¿²¢ËµÃ÷ÀíÓÉ£»
£¨3£©µ±µãMÔ˶¯µ½Ê²Ã´Î»ÖÃʱ£¬ËıßÐÎOCMDµÄÃæ»ýÓÐ×î´óÖµ£¿×î´óÖµÊǶàÉÙ£¿
£¨4£©µ±ËıßÐÎOCMDΪÕý·½ÐÎʱ£¬½«ËıßÐÎOCMDÑØ×ÅxÖáµÄÕý·½ÏòÒƶ¯£¬ÉèƽÒƵľàÀëΪb£¨0£¼b£¼4£©£¬Õý·½ÐÎO¡äCMDÓë¡÷AOBÖصþ²¿·ÖµÄÃæ»ýΪS£®ÊÔÇóSÓëbµÄº¯Êý¹Øϵʽ²¢»­³ö¸Ãº¯ÊýµÄͼÏó£®

Answer 1

·ÖÎö£º£¨1£©°Ñµ±x=aʱ£¬´úÈëÖ±ÏߵĽâÎöʽ¼´¿ÉÇóµÃ×Ý×ø±ê£»
£¨2£©µãMµÄºá×ø±êΪx£¬ÔòµãMµÄ×Ý×ø±êΪ-x+4£¬ÀûÓÃPµÄ×ø±ê¼´¿É±íʾ³öËıßÐÎOCMDµÄÖܳ¤£¬È»ºó¶ÔÕûʽ½øÐл¯¼ò¼´¿ÉÇó½â£»
£¨3£©µãMµÄºá×ø±êΪx£¬ÔòµãMµÄ×Ý×ø±êΪ-x+4£¬ÀûÓÃPµÄ×ø±ê¼´¿É±íʾ³öËıßÐÎOCMDµÄÃæ»ý¼´¿É±íÉϳÉxµÄº¯Êý£¬ÀûÓú¯ÊýµÄÐÔÖʼ´¿ÉÇóµÃ×îÖµ£»
£¨4£©·ÖÁ½ÖÖÇé¿ö½øÐÐÌÖÂÛ£¬µ±Öغϲ¿·ÖÊÇÎå±ßÐÎʱ£¬Ãæ»ýÊÇÕý·½ÐÎÓë¡÷EFMµÄ²î£»Öغϲ¿·ÖÊÇÈý½ÇÐΣ¬ÀûÓÃÈý½ÇÐεÄÃæ»ý¹«Ê½¼´¿ÉµÃµ½º¯Êý½âÎöʽ£®

½â´ð£º½â£º£¨1£©µ±x=aʱ£¬´úÈëÖ±ÏߵĽâÎöʽµÃ£ºy=-a+4£®
¹Ê´ð°¸ÊÇ£º-a+4£»
£¨2£©ÉèµãMµÄºá×ø±êΪx£¬ÔòµãMµÄ×Ý×ø±êΪ-x+4£¨0£¼x£¼4£¬x£¾0£¬-x+4£¾0£©£»
Ôò£ºMC=|-x+4|=-x+4£¬MD=|x|=x£»
¡àC_{ËıßÐÎOCMD}=2£¨MC+MD£©=2£¨-x+4+x£©=8
¡àµ±µãMÔÚABÉÏÔ˶¯Ê±£¬ËıßÐÎOCMDµÄÖܳ¤²»·¢Éú±ä»¯£¬×ÜÊǵÈÓÚ8£»
£¨3£©¸ù¾ÝÌâÒâµÃ£ºS_{ËıßÐÎOCMD}=MC•MD=£¨-x+4£©•x=-x²+4x=-£¨x-2£©²+4
¡àËıßÐÎOCMDµÄÃæ»ýÊǹØÓÚµãMµÄºá×ø±êx£¨0£¼x£¼4£©µÄ¶þ´Îº¯Êý£¬²¢ÇÒµ±x=2£¬¼´µ±µãMÔ˶¯µ½Ï߶ÎABµÄÖеãʱ£¬ËıßÐÎOCMDµÄÃæ»ý×î´óÇÒ×î´óÃæ»ýΪ4£»
£¨4£©Èçͼ£¨2£©£¬µ±0£¼b¡Ü2ʱ£¬¡÷MEFÊǵÈÑüÖ±½ÇÈý½ÇÐΣ¬ME=b£¬£®
ÔòS=4-

1

2

b²=-

1

2

b²+4£»
Èçͼ10£¨3£©£¬µ±2¡Üb£¼4ʱ£¬¡÷AGHÊǵÈÑüÖ±½ÇÈý½ÇÐΣ¬AH=4-b£¬ÔòS=

1

2

£¨4-b£©²£»
¡àSÓëbµÄº¯ÊýµÄͼÏóÈçÏÂͼËùʾ£º

µãÆÀ£º±¾Ì⿼²éÁËÒ»´Îº¯ÊýÓë¶þ´Îº¯ÊýµÄÐÔÖÊ£¬ÕýÈ·Áгöº¯Êý½âÎöʽÊǹؼü£®