ÌâÄ¿ÄÚÈÝ
ÒÑÖªµã£¬¶¯µãN£¨x£¬y£©£¬ÉèÖ±ÏßNP£¬NQµÄбÂÊ·Ö±ð¼ÇΪk1£¬k2£¬¼Ç£¨ÆäÖС°?¡±¿ÉÒÔÊÇËÄÔòÔËËã¼Ó¡¢¼õ¡¢³Ë¡¢³ýÖеÄÈÎÒâÒ»ÖÖÔËË㣩£¬×ø±êÔµãΪO£¬µãM£¨2£¬1£©£®£¨¢ñ£©Ì½Ç󶯵ãNµÄ¹ì¼£·½³Ì£»
£¨¢ò£©Èô¡°?¡±±íʾ³Ë·¨£¬¶¯µãNµÄ¹ì¼£ÔÙ¼ÓÉÏP£¬QÁ½µã¼ÇΪÇúÏßC£¬Ö±ÏßlƽÐÐÓÚÖ±ÏßOM£¬ÇÒÓëÇúÏßC½»ÓÚA£¬BÁ½¸ö²»Í¬µÄµã£®
£¨¢¡£©ÈôÔµãOÔÚÒÔABΪֱ¾¶µÄÔ²µÄÄÚ²¿£¬ÊÔÇó³öÖ±ÏßlÔÚyÖáÉϵĽؾàmµÄÈ¡Öµ·¶Î§£®
£¨¢¢£©ÊÔÇó³ö¡÷AOBÃæ»ýµÄ×î´óÖµ¼°´ËʱֱÏßlµÄ·½³Ì£®
¡¾´ð°¸¡¿·ÖÎö£º£¨¢ñ£©ÓÉбÂʹ«Ê½Ö±½Óд³ök1£¬k2£¬È»ºóÖ±½ÓÀûÓüӣ¬¼õ£¬³Ë£¬³ýÔËËãÕûÀíµÃ¶¯µãNµÄ¹ì¼£·½³Ì£»
£¨¢ò£©£¨¢¡£©Éè³öÖ±ÏßlµÄ·½³Ì£¬ºÍÍÖÔ²·½³ÌÁªÁ¢ºó»¯Îª¹ØÓÚxµÄÒ»Ôª¶þ´Î·½³Ì£¬ÀûÓøùÓëϵÊý¹ØϵµÃµ½Á½½»µãA£¬BµÄºá×ø±êµÄºÍÓë»ý£¬ÀûÓÃÔµãOÔÚÒÔABΪֱ¾¶µÄÔ²µÄÄÚ²¿µÃµ½£¬´úÈë¸ùÓëϵÊý¹Øϵ¼´¿ÉÇóµÃmµÄ·¶Î§£»
£¨¢¢£©ÀûÓÃÏÒ³¤¹«Ê½Çó³öÏÒ³¤£¬Óɵ㵽ֱÏߵľàÀ빫ʽÇó³öÈý½ÇÐεĸߣ¬´úÈëÃæ»ý¹«Ê½ºóÀûÓÃÅä·½·¨Çó×îÖµ£¬²¢µÃµ½Èý½ÇÐÎÃæ»ý×î´óʱµÄÖ±Ïß·½³Ì£®
½â´ð£º½â£º£¨¢ñ£©ÓÉÁ½µãÇóбÂʵã¬
µ±¡°?¡±±íʾ¼Ó·¨Ê±£º£®
µ±¡°?¡±±íʾ¼õ·¨Ê±£º£®
µ±¡°?¡±±íʾ³Ë·¨Ê±£º£®
µ±¡°?¡±±íʾ³Ë·¨Ê±£º£»
£¨¢ò£©Èô¡°?¡±±íʾ³Ë·¨£¬ÇúÏßCΪÍÖÔ²£¬
ÉèÖ±ÏßA£¨x1£¬y1£©£¬B£¨x2£¬y2£©
ÁªÁ¢Ö±ÏßÓëÍÖÔ²µÄ·½³ÌµÃ£ºx2+2mx+2m2-4=0£¬
ÓÉ¡÷£¾0⇒0£¼m2£¼4£¬
¡£¨*£©
£¨¢¡£©ÒòΪµãOÔÚÒÔABΪֱ¾¶µÄÔ²ÄÚ£¬¹Ê£¬
¡à£¬
½«£¨*£©´úÈëµÃ
ËùÒÔmµÃÈ¡Öµ·¶Î§Îª£º
£¨¢¢£©ÔµãOµ½Ö±ÏßlµÄ¾àÀ룬
ÏÒ³¤
£¬
Áîf£¨m£©=4m2-m4=-£¨m2-2£©2+4¡Ê£¨0£¬4]
¹ÊµÃµ±ÇÒ½öµ±m2=2£¬¼´Ê±£¬
Ãæ»ýµÄ×î´óÖµSmax=2£®
´ËʱµÄÖ±ÏßlµÄ·½³ÌΪ£º£®
µãÆÀ£º±¾Ì⿼²éÁ˹켣·½³ÌµÄÇ󷨣¬¿¼²éÁËÖ±ÏßÓëԲ׶ÇúÏߵĹØϵ£¬¿¼²éÁËÊýѧת»¯Ë¼Ïë·½·¨£¬°ÑÔµãOÔÚÒÔABΪֱ¾¶µÄÔ²µÄÄÚ²¿×ª»¯ÎªÊýÁ¿»ýСÓÚ0Êǽâ´ð¸ÃÌâµÄ¹Ø¼ü£¬¿¼²éÁËѧÉúµÄ¼ÆËãÄÜÁ¦£¬ÊÇÓÐÒ»¶¨ÄѶÈÌâÄ¿£®
£¨¢ò£©£¨¢¡£©Éè³öÖ±ÏßlµÄ·½³Ì£¬ºÍÍÖÔ²·½³ÌÁªÁ¢ºó»¯Îª¹ØÓÚxµÄÒ»Ôª¶þ´Î·½³Ì£¬ÀûÓøùÓëϵÊý¹ØϵµÃµ½Á½½»µãA£¬BµÄºá×ø±êµÄºÍÓë»ý£¬ÀûÓÃÔµãOÔÚÒÔABΪֱ¾¶µÄÔ²µÄÄÚ²¿µÃµ½£¬´úÈë¸ùÓëϵÊý¹Øϵ¼´¿ÉÇóµÃmµÄ·¶Î§£»
£¨¢¢£©ÀûÓÃÏÒ³¤¹«Ê½Çó³öÏÒ³¤£¬Óɵ㵽ֱÏߵľàÀ빫ʽÇó³öÈý½ÇÐεĸߣ¬´úÈëÃæ»ý¹«Ê½ºóÀûÓÃÅä·½·¨Çó×îÖµ£¬²¢µÃµ½Èý½ÇÐÎÃæ»ý×î´óʱµÄÖ±Ïß·½³Ì£®
½â´ð£º½â£º£¨¢ñ£©ÓÉÁ½µãÇóбÂʵã¬
µ±¡°?¡±±íʾ¼Ó·¨Ê±£º£®
µ±¡°?¡±±íʾ¼õ·¨Ê±£º£®
µ±¡°?¡±±íʾ³Ë·¨Ê±£º£®
µ±¡°?¡±±íʾ³Ë·¨Ê±£º£»
£¨¢ò£©Èô¡°?¡±±íʾ³Ë·¨£¬ÇúÏßCΪÍÖÔ²£¬
ÉèÖ±ÏßA£¨x1£¬y1£©£¬B£¨x2£¬y2£©
ÁªÁ¢Ö±ÏßÓëÍÖÔ²µÄ·½³ÌµÃ£ºx2+2mx+2m2-4=0£¬
ÓÉ¡÷£¾0⇒0£¼m2£¼4£¬
¡£¨*£©
£¨¢¡£©ÒòΪµãOÔÚÒÔABΪֱ¾¶µÄÔ²ÄÚ£¬¹Ê£¬
¡à£¬
½«£¨*£©´úÈëµÃ
ËùÒÔmµÃÈ¡Öµ·¶Î§Îª£º
£¨¢¢£©ÔµãOµ½Ö±ÏßlµÄ¾àÀ룬
ÏÒ³¤
£¬
Áîf£¨m£©=4m2-m4=-£¨m2-2£©2+4¡Ê£¨0£¬4]
¹ÊµÃµ±ÇÒ½öµ±m2=2£¬¼´Ê±£¬
Ãæ»ýµÄ×î´óÖµSmax=2£®
´ËʱµÄÖ±ÏßlµÄ·½³ÌΪ£º£®
µãÆÀ£º±¾Ì⿼²éÁ˹켣·½³ÌµÄÇ󷨣¬¿¼²éÁËÖ±ÏßÓëԲ׶ÇúÏߵĹØϵ£¬¿¼²éÁËÊýѧת»¯Ë¼Ïë·½·¨£¬°ÑÔµãOÔÚÒÔABΪֱ¾¶µÄÔ²µÄÄÚ²¿×ª»¯ÎªÊýÁ¿»ýСÓÚ0Êǽâ´ð¸ÃÌâµÄ¹Ø¼ü£¬¿¼²éÁËѧÉúµÄ¼ÆËãÄÜÁ¦£¬ÊÇÓÐÒ»¶¨ÄѶÈÌâÄ¿£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿