ÔĶÁÏÂÁнâÌâ¹ý³Ì£º
ÌâÄ¿£ºÒÑÖª·½³Ìx2+mx+1=0µÄÁ½¸öʵÊý¸ùÊÇp¡¢q£¬ÊÇ·ñ´æÔÚmµÄÖµ£¬Ê¹µÃp¡¢qÂú×ã
1
p
+
1
q
=1
£¿Èô´æÔÚ£¬Çó³ömµÄÖµ£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®
½â£º´æÔÚÂú×ãÌâÒâµÄmÖµ£®ÓÉÒ»Ôª¶þ´Î·½³ÌµÄ¸ùÓëϵÊýµÄ¹ØϵµÃ
p+q=m£¬pq=1£®¡à
1
p
+
1
q
=
p+q
pq
=
m
1
=m
£®¡ß
1
p
+
1
q
=1
£¬¡àm=1£®
ÔĶÁºó»Ø´ðÏÂÁÐÎÊÌ⣺ÉÏÃæµÄ½âÌâ¹ý³ÌÊÇ·ñÕýÈ·£¿Èô²»ÕýÈ·£¬Ð´³öÕýÈ·µÄ½âÌâ¹ý³Ì£®
·ÖÎö£ºÓÉÁ½¸ùÖ®ºÍ=-
b
a
£¬Ëã³ömµÄÖµºó£¬Ó¦¸ù¾Ý¸ùµÄÅбðʽÅжϷ½³ÌÊÇ·ñÓиù£®
½â´ð£º½â£º²»ÕýÈ·£®
ÕýÈ·µÄ½âÌâ¹ý³ÌÈçÏ£º
²»´æÔÚÂú×ãÌâÒâµÄmµÄÖµ£¬ÀíÓÉÊÇ£º
ÓÉÒ»Ôª¶þ´Î·½³ÌµÄ¸ùÓëϵÊýµÄ¹ØϵµÃp+q=-m£¬pq=1£®
¡à
1
P
+
1
q
=
p+q
pq
=
-m
1
=-m£®
¡ß
1
p
+
1
q
=1£®
¡àm=-1£®
µ±m=-1ʱ£¬¡÷=m2-4=-3£¼0£¬´Ëʱ·½³ÌÎÞʵÊý¸ù£®
¡à²»´æÔÚÂú×ãÌâÒâµÄmµÄÖµ£®
µãÆÀ£º±¾ÌâÓõ½µÄ֪ʶµãΪ£ºÒ»Ôª¶þ´Î·½³ÌÈôÓÐʵÊý¸ù£¬ÔòÁ½¸ùÖ®ºÍ=-
b
a
£¬Á½¸ùÖ®»ý=
c
a
£»¸ùµÄÅбðʽСÓÚ0£¬Ô­·½³ÌÎ޽⣮
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÔĶÁÀí½â

¾«Ó¢¼Ò½ÌÍø£¨ÌåÑé̽¾¿Ì⣩ÔĶÁÏÂÁнâÌâ¹ý³Ì²¢Ìî¿Õ£®
ÈçͼËùʾ£¬ÊÇÒ»¸öתÅÌ£¬×ªÅÌ·Ö³ÉÁË6¸öÏàͬµÄÉÈÐΣ¬ÉÈÉ«Óк졢»Æ¡¢À¶ÈýÖÖÑÕÉ«£¬Ö¸ÕëµÄλÖù̶¨£¬×ª¶¯×ªÅ̺óÈÃÆä×Ô¶¯Í£Ö¹£¬ÆäÖеÄij¸öÉÈÐλáÇ¡ºÃÍ£ÔÚÖ¸ÕëËùÔÚµÄλÖã¬ÇóÏÂÁÐʼþµÄ¸ÅÂÊ£®
£¨1£©Ê¼þA£¬Ö¸ÕëÖ¸ÏòºìÉ«£®
£¨2£©Ê¼þB£¬Ö¸ÕëÖ¸ÏòºìÉ«»òÀ¶É«£®
½â£ºÉèÿ¸öÉÈÐÎÃæ»ýΪ1¸öµ¥Î»£¬ÎÊÌâÖпÉÄܳöÏֵľùµÈ½á¹ûÓÐ6ÖÖÇé¿ö£¬ËùÒÔn=6£¨µ¥Î»£©£®
£¨1£©Ö¸ÕëÖ¸ÏòºìÉ«£¬³öÏÖºìÉ«ËùÕ¼Ãæ»ým1£¬Ôòm1=
 
£¬P£¨A£©=
m1
n
=
 
£®
£¨2£©Ö¸ÕëÖ¸ÏòÀ¶É«»òºìÉ«£¬ºìÉ«£¬À¶É«ËùÕ¼Ãæ»ým2=
 
£¬P£¨B£©=
m2
n
=
 
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨i£©ÓÐÕâÑùÒ»µÀÌ⣺¡°
x2-2x+1
x2-1
¡Â
x-1
x2+x
-x
£¬ÆäÖÐx=2007¡±¼×ͬѧ°Ñ¡°x=2007¡±´í³­³É¡°x=2070¡±£¬µ«Ëû¼ÆËãµÄ½á¹ûÒ²ÊÇÕýÈ·µÄ£¬Äã˵ÕâÊÇÔõôһ»ØÊ£¿

£¨ii£©ÔĶÁÏÂÁнâÌâ¹ý³Ì£¬²¢Ìî¿Õ£º
½â·½³Ì
1
x+2
+
4x
(x+2)(x-2)
=
2
2-x

½â£º·½³ÌÁ½±ßͬʱ³ËÒÔ£¨x+2£©£¨x-2£©
È¥·ÖĸµÃ£º¢Ù
£¨x-2£©+4x=2£¨x+2£©¢Ú
È¥À¨ºÅ£¬ÒÆÏîµÃ
x-2+4x-2x-4=0    ¢Û
½âÕâ¸ö·½³ÌµÃx=2¢Ü
ËùÒÔx=2ÊÇÔ­·½³ÌµÄ½â¢ÝÎÊÌ⣺£¨1£©ÉÏÊö¹ý³ÌÊÇ·ñÕýÈ·´ð£º
 
£®
£¨2£©ÈôÓÐ´í£¬´íÔÚµÚ
 
²½£®
£¨3£©´íÎóµÄÔ­ÒòÊÇ
 

£¨4£©¸Ã²½¸ÄÕýΪ
 
£®

£¨iii£©EÊÇÕý·½ÐÎABCDµÄ¶Ô½ÇÏßBDÉÏÒ»µã£¬EF¡ÍBC£¬EG¡ÍCD£¬´¹×ã·Ö±ðÊÇF¡¢G£®ÇóÖ¤£ºAE=FG£¬
¾«Ó¢¼Ò½ÌÍø

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÔĶÁÀí½â

ÔĶÁÀí½âÌâ
ÔĶÁÏÂÁнâÌâ¹ý³Ì£¬²¢°´ÒªÇóÌî¿Õ£º
ÒÑÖª£º
(2x-y)2
=1£¬
3(x-2y)3
=-1£¬Çó
3x+y
x-y
µÄÖµ£®
½â£º¸ù¾ÝËãÊõƽ·½¸ùµÄÒâÒ壬ÓÉ
(2x-y)2
=1£¬µÃ£¨2x-y£©2=1£¬2x-y=1µÚÒ»²½
¸ù¾ÝÁ¢·½¸ùµÄÒâÒ壬ÓÉ
3(x-2y)3
=-1£¬µÃx-2y=-1¡­µÚ¶þ²½
ÓÉ¢Ù¡¢¢Ú£¬µÃ
2x-y=1
x-2y=1
£¬½âµÃ
x=1
y=1
¡­µÚÈý²½
°Ñx¡¢yµÄÖµ·Ö±ð´úÈë·Öʽ
3x+y
x-y
ÖУ¬µÃ
3x+y
x-y
=0     ¡­µÚËIJ½
ÒÔÉϽâÌâ¹ý³ÌÖÐÓÐÁ½´¦´íÎó£¬Ò»´¦ÊǵÚ
 
²½£¬ºöÂÔÁË
 
£»Ò»´¦ÊǵÚ
 
²½£¬ºöÂÔÁË
 
£»ÕýÈ·µÄ½áÂÛÊÇ
 
£¨Ö±½Óд³ö´ð°¸£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÔĶÁÀí½â

ÔĶÁÀí½âÏÂÁи÷Ì⣬²¢°´ÒªÇó½â´ð£º
£¨1£©ÔĶÁÏÂÁнâÌâ¹ý³Ì£º
1
2
+1
=
1•(
2
-1)
(
2
+1)(
2
-1)
=
2
-1
(
2
)
2
-12
=
2
-1
£»
1
3
+
2
=
1•(
3
-
2
)
(
3
+
2
)(
3
-
2
)
=
3
-
2
(
3
)
2
-(
2
)
2
=
3
-
2

Çë»Ø´ðÏÂÁи÷ÎÊÌâ
¢Ù¹Û²ìÉÏÃæ½âÌâ¹ý³Ì£¬ÄãÄÜÖ±½Ó¸ø³ö
1
n
+
n-1
µÄ½á¹ûÂð£¿
¢ÚÀûÓÃÉÏÃæÌṩµÄ·½·¨£¬ÄãÄÜ»¯¼òÏÂÃæµÄʽ×ÓÂð£¿
1
1+
2
+
1
2
+
3
+¡­+
1
98
+
99
+
1
99
+
100

£¨2£©¡°Ò»×é¶Ô±ßƽÐУ¬ÁíÒ»×é¶Ô±ßÏàµÈµÄËıßÐÎÊÇƽÐÐËıßÐΡ±¶ÔÂð£¿Èç¹û²»¶Ô£¬Çë¾Ù·´Àý˵Ã÷£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º³õÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÔĶÁÏÂÁнâÌâ¹ý³Ì£º
1
5
+
4
=
1¡Á(
5
-
4
)
(
5
+
4
)(
5
-
4
)
=
5
-
4
(
5
)
2
-(
4
)
2
=
5
-
4
£¬
1
6
+
5
=
1¡Á(
6
-
5
)
(
6
+
5
)(
6
-
5
)
=
6
-
5
(
6
)
2
-(
5
)
2
=
6
-
5
£¬
Çë»Ø´ðÏÂÁлØÌ⣺
£¨1£©¹Û²ìÉÏÃæµÄ½â´ð¹ý³Ì£¬ÇëÖ±½Óд³ö
1
n+1
+
n
=
n+1
-
n
n+1
-
n
£»
£¨2£©¸ù¾ÝÉÏÃæµÄ½â·¨£¬Ç뻯¼ò£º
1
1+
2
+
1
2
+
3
+
1
3
+
4
+¡­+
1
98
+
99
+
1
99
+
100
£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸