Question

3£®Èçͼ1ÊÇÒ»¸ö³¤Îª4a¡¢¿íΪbµÄ³¤·½ÐΣ¬ÑØͼÖÐÐéÏßÓüôµ¶Æ½¾ù·Ö³ÉËÄ¿éС³¤·½ÐΣ¬È»ºóÓÃËÄ¿éС³¤·½ÐÎÆ´³ÉµÄÒ»¸ö¡°»ØÐΡ±Õý·½ÐΣ¨Èçͼ2£©£®

£¨1£©Í¼¢ÚÖеÄÒõÓ°²¿·ÖµÄÃæ»ýΪ£¨b-a£©²£»
£¨2£©¹Û²ìͼ¢ÚÇëÄãд³ö £¨a+b£©²£¬£¨a-b£©²£¬abÖ®¼äµÄµÈÁ¿¹ØϵÊÇ£¨a+b£©²-£¨a-b£©²=4ab£»
£¨3£©¸ù¾Ý£¨2£©ÖеĽáÂÛ£¬Èôx+y=4£¬xy=$\frac{9}{4}$£¬Ôò£¨x-y£©²=7£»
£¨4£©Êµ¼ÊÉÏͨ¹ý¼ÆËãͼÐεÄÃæ»ý¿ÉÒÔ̽ÇóÏàÓ¦µÄµÈʽ£®Èçͼ¢Û£¬Äã·¢ÏֵĵÈʽÊÇ£¨a+b£©•£¨3a+b£©=3a²+4ab+b²£®

Answer 1

·ÖÎö £¨1£©ÒõÓ°²¿·ÖΪ±ß³¤Îª£¨b-a£©µÄÕý·½ÐΣ¬È»ºó¸ù¾ÝÕý·½ÐεÄÃæ»ý¹«Ê½Çó½â£»
£¨2£©ÔÚͼ2ÖУ¬´óÕý·½ÐÎÓÐСÕý·½ÐκÍ4¸ö¾ØÐÎ×é³É£¬Ôò£¨a+b£©²-£¨a-b£©²=4ab£»    
£¨3£©ÓÉ£¨2£©µÄ½áÂ۵õ½£¨x+y£©²-£¨x-y£©²=4xy£¬ÔÙ°Ñx+y=4£¬x•y=$\frac{9}{4}$µÃµ½£¨x-y£©²=7£»
£¨4£©¹Û²ìͼÐεõ½±ß³¤Îª£¨a+b£©Ó루3a+b£©µÄ¾ØÐÎÓÉ3¸ö±ß³¤ÎªaµÄÕý·½ÐΡ¢4¸ö±ß³¤Îªa¡¢bµÄ¾ØÐκÍÒ»¸ö±ß³¤ÎªbµÄÕý·½ÐÎ×é³É£¬ÔòÓУ¨a+b£©•£¨3a+b£©=3a²+4ab+b²£®

½â´ð ½â£º£¨1£©ÒõÓ°²¿·ÖΪ±ß³¤Îª£¨b-a£©µÄÕý·½ÐΣ¬ËùÒÔÒõÓ°²¿·ÖµÄÃæ»ý£¨b-a£©²£¬
¹Ê´ð°¸Îª£º£¨b-a£©²£»

£¨2£©Í¼2ÖУ¬Óñ߳¤Îªa+bµÄÕý·½ÐεÄÃæ»ý¼õÈ¥±ß³¤Îªb-aµÄÕý·½ÐεÈÓÚ4¸ö³¤¿í·Ö±ða¡¢bµÄ¾ØÐÎÃæ»ý£¬
ËùÒÔ£¨a+b£©²-£¨a-b£©²=4ab£¬
¹Ê´ð°¸Îª£º£¨a+b£©²-£¨a-b£©²=4ab£»    

£¨3£©¡ß£¨x+y£©²-£¨x-y£©²=4xy£¬
¶øx+y=4£¬x•y=$\frac{9}{4}$£¬
¡à4²-£¨x-y£©²=4¡Á$\frac{9}{4}$£¬
¡à£¨x-y£©²=7£¬
¹Ê´ð°¸Îª£º7£»

£¨4£©±ß³¤Îª£¨a+b£©Ó루3a+b£©µÄ¾ØÐÎÃæ»ýΪ£¨a+b£©£¨3a+b£©£¬ËüÓÉ3¸ö±ß³¤ÎªaµÄÕý·½ÐΡ¢4¸ö±ß³¤Îªa¡¢bµÄ¾ØÐκÍÒ»¸ö±ß³¤ÎªbµÄÕý·½ÐÎ×é³É£¬
¡à£¨a+b£©•£¨3a+b£©=3a²+4ab+b²£®
¹Ê´ð°¸Îª£º£¨a+b£©•£¨3a+b£©=3a²+4ab+b²£®

µãÆÀ ±¾Ì⿼²éÁËÍêȫƽ·½¹«Ê½µÄ¼¸ºÎ±³¾°£ºÀûÓÃÃæ»ý·¨Ö¤Ã÷Íêȫƽ·½¹«Ê½£¨a-b£©²=a²-2ab+b²£®