8£®ÀûÓÃÎÒÃÇѧ¹ýµÄ֪ʶ£¬¿ÉÒÔµ¼³öÏÂÃæÕâ¸öÐÎʽÓÅÃÀµÄµÈʽ£ºa2+b2+c2-ab-bc-ac=$\frac{1}{2}$[£¨a-b£©2+£¨b-c£©2+£¨c-a£©2]£¬¸ÃµÈʽ´Ó×óµ½ÓҵıäÐΣ¬²»½ö±£³ÖÁ˽ṹµÄ¶Ô³ÆÐÔ£¬»¹ÌåÏÖÁËÊýѧµÄºÍг¡¢¼ò½àÃÀ£®
£¨1£©ÇëÄã¼ìÑéÕâ¸öµÈʽµÄÕýÈ·ÐÔ£»
£¨2£©Èôa=2012£¬b=2013£¬c=2014£¬ÄãÄܺܿìÇó³öa2+b2+c2-ab-bc-acµÄÖµÂð£¿

·ÖÎö £¨1£©ÒÑÖªµÈʽÓÒ±ßÀûÓÃÍêȫƽ·½¹«Ê½»¯¼ò£¬ÕûÀí¼´¿É×÷³öÑéÖ¤£»
£¨2£©°Ña£¬b£¬cµÄÖµ´úÈëÒÑÖªµÈʽÓұߣ¬Çó³öÖµ¼´ÎªËùÇóʽ×ÓµÄÖµ£®

½â´ð £¨1£©Ö¤Ã÷£ºÓÒ±ß=$\frac{1}{2}$[£¨a-b£©2+£¨b-c£©2+£¨c-a£©2]=$\frac{1}{2}$£¨a2-2ab+b2+b2-2bc+c2+c2-2ac+a2£©=$\frac{1}{2}$£¨2a2+2b2+2c2-2ab-2bc-2ac£©=a2+b2+c2-ab-bc-ac=×ó±ß£»
£¨2£©½â£ºµ±a=2012£¬b=2013£¬c=2014ʱ£¬Ô­Ê½=$\frac{1}{2}$[£¨a-b£©2+£¨b-c£©2+£¨c-a£©2]=$\frac{1}{2}$¡Á£¨1+1+4£©=3£®

µãÆÀ ´ËÌ⿼²éÁËÍêȫƽ·½¹«Ê½£¬ÊìÁ·ÕÆÎÕÍêȫƽ·½¹«Ê½ÊǽⱾÌâµÄ¹Ø¼ü£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

18£®£¨1£©Èçͼ1£¬½«Á½ÕÅÕý·½ÐÎֽƬAÓëÈýÕÅÕý·½ÐÎֽƬB·ÅÔÚÒ»Æ𣨲»ÖصþÎÞ·ì϶£©£¬Æ´³ÉÒ»¸ö¿íΪ10µÄ³¤·½ÐΣ¬ÇóÕý·½ÐÎֽƬA¡¢BµÄ±ß³¤£®
£¨2£©Èçͼ2£¬½«Ò»ÕÅÕý·½ÐÎֽƬD·ÅÔÚÒ»Õý·½ÐÎֽƬCµÄÄÚ²¿£¬ÒõÓ°²¿·ÖµÄÃæ»ýΪ4£»Èçͼ3£¬½«Õý·½ÐÎֽƬC¡¢D¸÷Ò»ÕŲ¢ÁзÅÖúó¹¹ÔìÒ»¸öеÄÕý·½ÐΣ¬ÒõÓ°²¿·ÖµÄÃæ»ýΪ48£¬ÇóÕý·½ÐÎC¡¢DµÄÃæ»ýÖ®ºÍ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

19£®Èçͼ£¬ÒÑÖª¡÷ABC¡Õ¡÷DCE¡Õ¡÷HEF£¬ÈýÌõ¶ÔÓ¦±ßBC¡¢CE¡¢EFÔÚͬһÌõÖ±ÏßÉÏ£¬Á¬½ÓBH£¬·Ö±ð½»AC¡¢DC¡¢DEÓÚµãP¡¢Q¡¢K£¬ÆäÖÐS¡÷PQC=1£¬ÔòͼÖÐÈý¸öÒõÓ°²¿·ÖµÄÃæ»ýºÍΪ13£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

16£®ÒÑÖª£ºx3+px+qÄܱ»£¨x-a£©2Õû³ý£¬ÇóÖ¤£º4p3+27q2=0£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

3£®Èçͼ£¬Îª²âÁ¿Ð¡ºÓµÄ¿í¶È£¬ÏÈÔÚºÓ°¶±ßÈÎÈ¡Ò»µãA£¬ÔÙÔÚºÓµÄÁíÒ»°¶±ßÈ¡Á½µãB£¬C£¬²âµÃ¡ÏABC=60¡ã£¬¡ÏACB=30¡ã£¬Á¿µÃBCµÄ³¤Îª20m£¬ABµÄ³¤ÎªBC³¤µÄÒ»°ë£¬ÇóСºÓµÄ¿í¶È£®£¨½á¹û±£Áô¸ùºÅ£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

13£®Èçͼ£¬ÔÚ¡÷ABCÖУ¬AB=AC£¬¸ßADºÍBEÏཻÓÚµãH£¬ÇÒAH=2BD£¬ÇóÖ¤£ºAE=BE£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

20£®Èçͼ£¬AEƽ·Ö¡ÏBAC½»BCÓÚµãD£¬¡ÏC=¡ÏEBC£¬¡ÏBAC=70¡ã£¬¡ÏABC=30¡ã£¬Çó¡ÏEºÍ¡ÏADCµÄ¶ÈÊý£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

17£®Èô¼Çy=f£¨x£©=$\frac{{x}^{2}}{1+{x}^{2}}$£¬ÆäÖÐf£¨1£©±íʾµ±x=1ʱyµÄÖµ£¬¼´f£¨1£©=$\frac{{1}^{2}}{1+{1}^{2}}$=$\frac{1}{2}$£»
f£¨$\frac{1}{2}$£©±íʾµ±x=$\frac{1}{2}$ʱyµÄÖµ£¬¼´f£¨$\frac{1}{2}$£©=$\frac{£¨\frac{1}{2}£©^{2}}{1+£¨\frac{1}{2}£©^{2}}$=$\frac{1}{5}$¡­£»
Ôòf£¨1£©+f£¨2£©+f£¨$\frac{1}{2}$£©+f£¨3£©+f£¨$\frac{1}{3}$£©+¡­+f£¨2016£©+f£¨$\frac{1}{2016}$£©=2015.5£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

7£®ÈçͼËùʾµÄÊÇÓÉ5¸ö±ß³¤ÊÇ1µÄÕý·½ÐÎ×é³ÉµÄͼÐΣ®
£¨1£©ÇóBA12£¬BA22£¬BA32µÄÖµ£»
£¨2£©´Ó£¨1£©ÖÐÑ°ÕÒ¹æÂÉ£¬µ±ÓÐ10¸öÕý·½ÐÎʱ£¬ÇóBA102µÄÖµ£»
£¨3£©µ±ÓÐn¸öÕý·½ÐÎʱ£¬ÇóBAn2µÄÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸