Question

9£®Èçͼ£¬ÓÐ×ã¹»¶àµÄ±ß³¤ÎªaµÄСÕý·½ÐΣ¨AÀࣩ¡¢¿íΪa³¤ÎªbµÄ³¤·½ÐΣ¨BÀࣩÒÔ¼°±ß³¤ÎªbµÄ´óÕý·½ÐΣ¨CÀࣩ£¬·¢ÏÖÀûÓÃͼ¢ÙÖеÄÈýÖÖ²ÄÁÏÈô¸É¿ÉÒÔÆ´³öһЩ³¤·½ÐÎÀ´½âÊÍijЩµÈʽ£®
³¢ÊÔ½â¾ö£º£¨1£©È¡Í¼¢ÙÖеÄÈô¸É¸ö£¨ÈýÀàͼÐζ¼ÒªÈ¡µ½£©Æ´³ÉÒ»¸ö³¤·½ÐΣ¬Ê¹ÆäÃæ»ýΪ£¨a+b£©£¨a+b£©£¬ÔÚÏÂÃæÐéÏß¿òÖл­³öͼÐΣ¬²¢¸ù¾ÝͼÐλشð£¨a+b£©£¨a+b£©=a²+2ab+b²£®
£¨2£©Í¼¢ÚÊÇÓÉͼ¢ÙÖеÄÈýÖÖ²ÄÁÏÆ´³öµÄÒ»¸ö³¤·½ÐΣ¬¸ù¾Ý¢Ú¿ÉÒԵõ½²¢½âÊ͵Èʽ£ºa²+3ab+2b²£®
£¨3£©ÈôÈ¡ÆäÖеÄÈô¸É¸ö£¨ÈýÀàͼÐζ¼ÒªÈ¡µ½£©Æ´³ÉÒ»¸ö³¤·½ÐΣ¬Ê¹ÆäÃæ»ýΪ3a²+4ab+b²£®
¢ÙÄã»­µÄͼÖÐÐèÒªBÀ࿨Ƭ4ÕÅ£»
¢Ú·Ö½âÒòʽ£º3a²+4ab+b²£®
ÍØÕ¹Ñо¿£ºÈçͼ¢Û£¬´óÕý·½Ðεı߳¤Îªm£¬Ð¡Õý·½Ðεı߳¤Îªn£¬ÈôÓÃm¡¢n±íʾËĸöÖ±½ÇÈý½ÇÐεÄÁ½Ö±½Ç±ß±ß³¤£¨¡¡b£¾a¡¡£©£¬¹Û²ìͼ°¸£¬ÒÔϹØϵʽÖÐÕýÈ·µÄÓУ¨1£©£¬£¨4£©£®£¨ÌîдÕýÈ·Ñ¡ÏîµÄÐòºÅ£©
£¨1£©ab=$\frac{{m}^{2}-{n}^{2}}{2}$£¨2£©a+b=m£¨3£©a²+b²=$\frac{{m}^{2}+{n}^{2}}{2}$£¨4£©a²+b²=m²

Answer 1

·ÖÎö £¨1£©»­³öͼÐΣ¬½áºÏͼÏóºÍÃæ»ý¹«Ê½µÃ³ö¼´¿É£»
£¨2£©¸ù¾ÝͼÐεÄÃæ»ý¼´¿ÉµÃµ½½áÂÛ£»
£¨3£©¢Ù¸ù¾ÝµÈʽ¼´¿ÉµÃ³öÓÐ3ÕÅ£¬¢Ú¸ù¾ÝÍêȫƽ·½¹«Ê½Åжϼ´¿É£®

½â´ð ½â£º£¨1£©Èçͼ£º
£¨a+b£©£¨a+b£©=a²+2ab+b²£®
¹Ê´ð°¸Îª£ºa²+2ab+b²£»

£¨2£©³¤·½ÐεÄÃæ»ýΪa²+3ab+2b²£¬
¹Ê´ð°¸Îª£ºa²+3ab+2b²£®

£¨3£©¢Ù¡ß3a²+4ab+b²=£¨3a+b£©£¨a+b£©£¬
¡àÐèÒªBÀ࿨Ƭ4ÕÅ£»
¹Ê´ð°¸Îª£º4£»

£¨3£©½â£º¸ù¾Ýͼ¢ÛµÃ£º4¡Á$\frac{1}{2}$ab+n²=m²£¬
¡àab=$\frac{{m}^{2}-{n}^{2}}{2}$£¬
¡ß£¨b-a£©²=n²£¬4¡Á$\frac{1}{2}$ab+n²=2ab+£¨b-a£©²=m²£¬
¡àa²+b²=m²£¬
¡à£¨1£©£¬£¨4£©ÕýÈ·£¬
¹Ê´ð°¸Îª£º£¨1£©£¬£¨4£©£®

µãÆÀ ±¾Ì⿼²éÁË·Ö½âÒòʽ£¬³¤·½ÐεÄÃæ»ý£¬Íêȫƽ·½¹«Ê½µÄÓ¦Óã¬Ö÷Òª¿¼²éѧÉúµÄ¹Û²ìͼÐεÄÄÜÁ¦ºÍ»¯¼òÄÜÁ¦£®