£¨2012•ÆÕÍÓÇøһģ£©ÉèµãFÊÇÅ×ÎïL£ºy2=2px£¨p£¾0£©µÄ½¹µã£¬P1£¬P2£¬¡­£¬PnÊÇÅ×ÎïÏßLÉϵÄn¸ö²»Í¬µÄµãn£¨n¡Ý3£¬n¡ÊN*£©£®
£¨1£©µ±p=2ʱ£¬ÊÔд³öÅ×ÎïÏßLÉÏÈýµãP1¡¢P2¡¢P3µÄ×ø±ê£¬Ê±ÆÚÂú×ã|
FP1
|+|
FP2
|+|
FP3
|=6
£»
£¨2£©µ±n¡Ý3ʱ£¬Èô
FP1
+
FP2
+¡­+
FPn
=
0
£¬ÇóÖ¤£º|
FP1
|+|
FP2
|+¡­+|
FPn
|=np
£»
£¨3£©µ±n£¾3ʱ£¬Ä³Í¬Ñ§¶Ô£¨2£©µÄÄæÃüÌ⣬¼´£º¡°Èô|
FP1
|+| 
FP2
|+¡­+|  
FPN
|=np
£¬Ôò
FP1
+
FP2
+¡­+
FPN
=
0
¡±¿ªÕ¹ÁËÑо¿²¢·¢ÏÖÆäΪ¼ÙÃüÌ⣮
ÇëÄã¾Í´Ë´ÓÒÔÏÂÈý¸öÑо¿·½ÏòÖÐÈÎÑ¡Ò»¸ö¿ªÕ¹Ñо¿£º
1£®ÊÔ¹¹ÔìÒ»¸ö˵Ã÷¸ÃÃüÌâȷʵÊǼÙÃüÌâµÄ·´Àý£»
2£®¶ÔÈÎÒâ¸ø¶¨µÄ´óÓÚ3µÄÕýÕûÊýn£¬ÊÔ¹¹Ôì¸Ã¼ÙÃüÌâ·´ÀýµÄÒ»°ãÐÎʽ£¬²¢ËµÃ÷ÄãµÄÀíÓÉ£º
3£®Èç¹û²¹³äÒ»¸öÌõ¼þºóÄÜʹ¸ÃÃüÌâΪÕ棬Çëд³öÄãÈÏΪÐèÒª²¹³äµÄÒ»¸öÌõ¼þ£¬²¢ËµÃ÷¼ÓÉϸÃÌõ¼þºó£¬ÄÜʹ¸ÃÄæÃüÌâΪÕæÃüÌâµÄÀíÓÉ£®
·ÖÎö£º£¨1£©Å×ÎïÏßlµÄ½¹µãΪF£¨
p
2
£¬0£©£¬ÉèP1£¨x1£¬y1£©£¬P2£¨x2£¬y2£©£¬P3£¨x3£¬y3£©£¬ÀûÓÃÅ×ÎïÏߵĶ¨Òå¿ÉµÃx1+x2+x3=3£¬¹Ê¿ÉÈ¡Âú×ãÌõ¼þµÄÈýµã£»
£¨2£©ÉèP1£¨x1£¬y1£©£¬P2£¨x2£¬y2£©£¬P3£¨x3£¬y3£©£¬¡­£¬Pn£¨xn£¬yn£©£¬·Ö±ð¹ýP1¡¢P2¡¢P3£¬¡­£¬Pn×÷Å×ÎïÏßµÄ×¼ÏßlµÄ´¹Ïߣ¬´¹×ã·Ö±ðΪQ1¡¢Q2¡¢Q3£¬¡­£¬Qn£¬ÀûÓÃÅ×ÎïÏߵĶ¨Òå¿ÉµÃx1+x2+x3+¡­+xn=
np
2
£¬´Ó¶ø¿ÉÖ¤
|FP1
|+|
FP2
|+¡­+|
FPn
|
=np
£¨3£©¢ÙÈ¡n=4ʱ£¬Å×ÎïÏßlµÄ½¹µãΪF£¨
p
2
£¬0£©£¬ÉèP1£¨x1£¬y1£©£¬P2£¨x2£¬y2£©£¬P3£¨x3£¬y3£©£¬P4£¨x4£¬y4£©£¬·Ö±ð¹ýP1¡¢P2¡¢P3£¬P4×÷Å×ÎïÏßµÄ×¼ÏßlµÄ´¹Ïߣ¬´¹×ã·Ö±ðΪQ1¡¢Q2¡¢Q3£¬Q4£¬ÀûÓÃÅ×ÎïÏߵĶ¨Ò壬¿ÉµÃx1+x2+x3+x4=2p£¬´Ó¶ø¿ÉµÃ½áÂÛ£»
¢ÚÉèP1£¨x1£¬y1£©£¬P2£¨x2£¬y2£©£¬P3£¨x3£¬y3£©£¬¡­£¬Pn£¨xn£¬yn£©£¬·Ö±ð¹ýP1¡¢P2¡¢P3£¬¡­£¬Pn×÷Å×ÎïÏßµÄ×¼ÏßlµÄ´¹Ïߣ¬´¹×ã·Ö±ðΪQ1¡¢Q2¡¢Q3£¬¡­£¬Qn£¬ÀûÓÃÅ×ÎïÏߵĶ¨Ò壬¿ÉµÃx1+x2+x3+¡­+xn=
np
2
£¬´Ó¶ø¿ÉµÃ½áÂÛ£»
¢Û²¹³äÌõ¼þ£ºµãPiµÄ×Ý×ø±êÂú×ãy1+y2+¡­+yn=0£¬¼´µ±n£¾3ʱ£¬|
FP1
|+| 
FP2
|+¡­+|  
FPn
|=np
£¬µãPiµÄ×Ý×ø±êÂú×ãy1+y2+¡­+yn=0£¬Ôò
FP1
+
FP2
+¡­+
FPn
=
0
£®
½â´ð£º½â£º£¨1£©Å×ÎïÏßlµÄ½¹µãΪF£¨
p
2
£¬0£©£¬ÉèP1£¨x1£¬y1£©£¬P2£¨x2£¬y2£©£¬P3£¨x3£¬y3£©£¬
·Ö±ð¹ýP1¡¢P2¡¢P3×÷Å×ÎïÏßµÄ×¼ÏßlµÄ´¹Ïߣ¬´¹×ã·Ö±ðΪQ1¡¢Q2¡¢Q3£¬
¡à|
FP1
|+|
FP2
|+|
FP3
|
=£¨x1+
p
2
£©+£¨x2+
p
2
£©+£¨x3+
p
2
£©=x1+x2+x3+
3p
2
=6
¡ßp=2£¬¡àx1+x2+x3=3
¹Ê¿ÉÈ¡P1£¨
1
2
£¬
2
£©£¬P2£¨1£¬2£©£¬P3£¨
3
2
£¬
6
£©Âú×ãÌõ¼þ£»
£¨2£©ÉèP1£¨x1£¬y1£©£¬P2£¨x2£¬y2£©£¬P3£¨x3£¬y3£©£¬¡­£¬Pn£¨xn£¬yn£©£¬·Ö±ð¹ýP1¡¢P2¡¢P3£¬¡­£¬Pn×÷Å×ÎïÏßµÄ×¼ÏßlµÄ´¹Ïߣ¬´¹×ã·Ö±ðΪQ1¡¢Q2¡¢Q3£¬¡­£¬Qn
¡à
|FP1
|+|
FP2
|+¡­+|
FPn
|
=£¨x1+
p
2
£©+£¨x2+
p
2
£©+£¨x3+
p
2
£©+¡­+£¨xn+
p
2
£©=x1+x2+x3+¡­+xn+
np
2

¡ß
FP1
+
FP2
+¡­+
FPn
=
0
           
¡àx1+x2+x3+¡­+xn=
np
2

¡à
|FP1
|+|
FP2
|+¡­+|
FPn
|
=
np
2
+
np
2
=np
£¨3£©¢ÙÈ¡n=4ʱ£¬Å×ÎïÏßlµÄ½¹µãΪF£¨
p
2
£¬0£©£¬ÉèP1£¨x1£¬y1£©£¬P2£¨x2£¬y2£©£¬P3£¨x3£¬y3£©£¬P4£¨x4£¬y4£©£¬·Ö±ð¹ýP1¡¢P2¡¢P3£¬P4×÷Å×ÎïÏßµÄ×¼ÏßlµÄ´¹Ïߣ¬´¹×ã·Ö±ðΪQ1¡¢Q2¡¢Q3£¬Q4£¬
¡à
|FP1
|+|
FP2
|+¡­+|
FP4
|
=x1+x2+x3+x4+2p=4p
¡àx1+x2+x3+x4=2p
²»·ÁÈ¡P1(
p
4
£¬
2
p
2
)
£¬P2(
p
2
£¬p)
£¬P3(
p
2
£¬-p)
£¬P4(
3p
4
£¬
6
p
2
)
£¬Ôò
FP1
+
FP2
+¡­+
FP4
¡Ù
0

¹ÊP1(
p
4
£¬
2
p
2
)
£¬P2(
p
2
£¬p)
£¬P3(
p
2
£¬-p)
£¬P4(
3p
4
£¬
6
p
2
)
ÊÇÒ»¸öµ±n=4ʱ£¬¸ÃÄæÃüÌâµÄÒ»¸ö·´Àý£»
¢ÚÉèP1£¨x1£¬y1£©£¬P2£¨x2£¬y2£©£¬P3£¨x3£¬y3£©£¬¡­£¬Pn£¨xn£¬yn£©£¬·Ö±ð¹ýP1¡¢P2¡¢P3£¬¡­£¬Pn×÷Å×ÎïÏßµÄ×¼ÏßlµÄ´¹Ïߣ¬´¹×ã·Ö±ðΪQ1¡¢Q2¡¢Q3£¬¡­£¬Qn
¡ß|
FP1
|+| 
FP2
|+¡­+|  
FPn
|=np
£¬¡àx1+x2+x3+¡­+xn+
np
2
=np£¬¡àx1+x2+x3+¡­+xn=
np
2

ÒòΪÉÏÊö±í´ïʽÓëµãµÄ×Ý×ø±êÎ޹أ¬ËùÒÔ½«Õânµã¶¼È¡ÔÚxÖáµÄÉÏ·½£¬ÔòËüÃǵÄ×Ý×ø±ê¶¼´óÓÚ0£¬Ôò
FP1
+
FP2
+¡­+
FPn
=£¨0£¬y1+y2+¡­+yn£©¡Ù
0

¢Û²¹³äÌõ¼þ£ºµãPiµÄ×Ý×ø±êÂú×ãy1+y2+¡­+yn=0£¬¼´µ±n£¾3ʱ£¬|
FP1
|+| 
FP2
|+¡­+|  
FPn
|=np
£¬µãPiµÄ×Ý×ø±êÂú×ãy1+y2+¡­+yn=0£¬Ôò
FP1
+
FP2
+¡­+
FPn
=
0

ÓÉ¢ÚÖª£¬ÃüÌâΪÕ森
µãÆÀ£º±¾Ì⿼²éÅ×ÎïÏߵĶ¨Ò壬¿¼²éÏòÁ¿µÄÔËË㣬½âÌâµÄ¹Ø¼üÊÇÕýÈ·ÔËÓÃÅ×ÎïÏߵĶ¨Ò壬ÄѶȽϴó£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2012•ÆÕÍÓÇøһģ£©
e
1
£¬
e
2
ÊÇÁ½¸ö²»¹²ÏßµÄÏòÁ¿£¬ÒÑÖª
AB
=2
e
1
+k
e
2
£¬
CB
=
e
1
+3
e
2
CD
=2
e
1
-
e
2
£¬ÇÒA£¬B£¬DÈýµã¹²Ïߣ¬ÔòʵÊýk=
-8
-8
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2012•ÆÕÍÓÇøһģ£©ÉèÈ«¼¯ÎªR£¬¼¯M={x|
x2
4
+y2=1
}£¬N={x|
x-3
x+1
¡Ü0
}£¬Ôò¼¯ºÏ{x|(x+
3
2
)
2
+y2=
1
4
}¿É±íʾΪ£¨¡¡¡¡£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2012•ÆÕÍÓÇøһģ£©ÒÑÖªÊýÁÐ{an}ÊÇÊ×ÏîΪ2µÄµÈ±ÈÊýÁУ¬ÇÒÂú×ãan+1=pan+2n(n¡ÊN*)
£¨1£©Çó³£ÊýpµÄÖµºÍÊýÁÐ{an}µÄͨÏʽ£»
£¨2£©Èô³éÈ¥ÊýÁÐÖеĵÚÒ»Ïî¡¢µÚËÄÏî¡¢µÚÆßÏî¡¢¡­µÚ3n-2Ï¡­£¬ÓàϵÄÏî°´Ô­À´µÄ˳Ðò×é³ÉÒ»¸öеÄÊýÁÐ{bn}£¬ÊÔд³öÊýÁÐ
{bn}µÄͨÏʽ£»
£¨3£©ÔÚ£¨2£©µÄÌõ¼þÏ£¬ÉèÊýÁÐ{bn}µÄÇ°nÏîºÍΪTn£¬ÊÇ·ñ´æÔÚÕýÕûÊýn£¬Ê¹µÃ
Tn+1
Tn
=
11
3
£¿Èô´æÔÚ£¬ÊÔÇóËùÓÐÂú×ãÌõ¼þµÄÕýÕûÊýnµÄÖµ£¬Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2012•ÆÕÍÓÇøһģ£©¶ÔÓÚƽÃæ¦Á¡¢¦Â¡¢¦ÃºÍÖ±Ïßa¡¢b¡¢m¡¢n£¬ÏÂÁÐÃüÌâÖÐÕæÃüÌâÊÇ£¨¡¡¡¡£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2012•ÆÕÍÓÇøһģ£©º¯Êýy=
1
log
1
2
|x-1|
µÄ¶¨ÒåÓòÊÇ
£¨0£¬1£©¡È£¨1£¬2£©
£¨0£¬1£©¡È£¨1£¬2£©
£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸