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ĐẠI HỌC QUỐC GIA HÀ NỘI
TRƯỜNG ĐẠI HỌC GIÁO DỤC ĐÀO THỊ PHƯƠNG THẢO

RÈN LUYỆN KỸ NĂNG GIẢI HỆ PHƯƠNG TRÌNH CHO
HỌC SINH KHÁ GIỎI TRUNG HỌC PHỔ THÔNG

LUẬN VĂN THẠC SĨ SƯ PHẠM TOÁN HÀ NỘI-2012

3

LỜI CẢM ƠN












Bắc Ninh, tháng 11 năm 2012
Tác giả Đào Thị Phương Thảo

 5
MỤC LỤC
Trang
MỞ ĐẦU
CHƯƠNG 1: CƠ SỞ LÍ LUẬN VÀ THỰC TIỄN ……………………
  
 

.
.


.



10
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

.
.
2
)






0)(
2121
2
 xxxxxx


 

49
57

69
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79

85
86
7


10,10 
nm
aathìnma

2.7.3. 
2.8. .
CHƯƠNG 3: THỰC NGHIỆM SƯ PHẠM ………………………




KẾT LUẬN …………………………………………………………
TÀI LIỆU THAM KHẢO …………………………………………

87

, 
“Giúp học sinh phát triển toàn diện về đạo đức, trí tuệ, thể chất, thẩm mĩ và các kĩ
năng cơ bản nhằm hình thành nhân cách con người Việt Nam Xã hội chủ nghĩa, xây
dựng tư cách và trách nhiệm công đồng, chuẩn bị cho học sinh tiếp tục học lên
hoặc đi vào cuộc sống lao động, tham gia xây dựng và bảo vệ tổ quốc”
  “phát huy tính tích cực,
tự giác, chủ động, sáng tạo của học sinh, phù hợp với đặc điểm của từng lớp học,
môn học; bồi dưỡng phương pháp tự học, rèn luyện kĩ năng vận dụng kiến thức vào
thực tiễn; tác động đến tình cảm, đem lại niềm vui, hứng thú học tập cho học sinh”.
Trong 
, cung , 

   

 


, , . 

 logarit. 
. 


. 
 c
 ,,  


4


5
+ 
7. 

 ,    ,       
 
, .
8. 


+ 



9. 




.
:  
1.1. K 
1.1.1. , 


 kĩ năng là năng lực sử dụng các dữ
kiện, các tri thức hay các khái niệm đã có, năng lực vận dụng chúng để phát hiện
những thuộc tính bản chất của các sự vật và giải quyết thành công nhiệm vụ lí luận
hay thực hành xác định”.
Theo2 “Kĩ năng là khả năng vận dụng tri thức





7
- 
 




- 

- 
- 



m


- 
 .
- 

- 
1.1.3. 

-  
.


inh.

1.6. 
   

 

9
 


.
: INH
2.1. 
2.1.1. 
2.1.2. 
2.1.3. 
2.1.4. 
2.2. 
2.2.1.  

.
 









)2(.0222
)1(0964
22
224
yxyx
yyxx

  

 
 
4
 





2.222
)1(1
yx
yx

:t
t.
10
2.2.2. 


xxyx
xyxyxx
(
:
(3)

.
7. 







)2(.2
)1(3
33
22
yxxy
xyyx







)2(.1)2(log)2(log
)1(24

2
-x
2
.
10. 







)2(.)1(51
)1(16411
22
33
xy
xyyx

11. 







.
1
2255











)2(.
2
9
)1(
3
16
x
y
xy
y
x
xy

2.3.2. 
3. 






t:  nhanh  
.
. 





.23
42
22
yxyx
yxxy

2.3.3. 
. 







.32
32
2
22
xyyx
xyx




(a-v)(u-b)=0. K
. 





.1
1
2
xyx
yxxy

 



3
22
 yxyx


. 












.1
1
22
yx
yxyxyx

13
. 





)2(.2
)1(331
22
yx
yxxy

2.4.2. 
0)(
2121
2
 xxxxxx

2 (1)
2 1 2 2 (2)
xy x y x y
x y y x x y
   



   


(2008).
 

 

22222
)(2 yxyxyxyyxyxxy 

0)1)(())(()()(  yxyyxyxyxyxyxy

0)12)((  xyyx
.
. 














)2(.75
)1(522
2
2
xxyy
yxyx

14
2.4.3.  

10. 







)2(.32
)1()1()12(2
2
23
yxx

222
322
yxyxxy
yxyxyyx
2011).

2.5. 




.
2.5.1. rong 
. 








)2(22
)1(2322
22
yxyx
yxyx
(2010).
. 



 



2.5.2. .
2.5.2.1. Đặt u = x + y, v = x – y
 







.13
12
23
22
xyx
yxy

 








11
22
22
yx
yx
yx
yx

4. 
















.)1(2)1(
4
1
1)(
22

22
22
22
xy
yx
xy
xy
yx
yx

2.5.2.3. Đặt
x
yv
y
xu
1
,
1


 











16
7. 



































.1
2
22
yx
yxyx

. 







.243232
5323
yxyx
yxyx






xyyx

:           
xypyxS  ,


xyyx ,
22


xyvyxu  ,
22
.
: .

2
22
18
( 1)( 1) 72
x y x y
xy x y

   

  


: 
t 
xy

18
( 1)( 1) 72
x y x y
xy x y

   

  

2.
2) Thay
22
,a x xy b y xy   

(2)
22
22
18
( ) 72
xy
xy x y








3) Thay

  


5) Thay
22
2,a x xy b y xy   

(5)
22
18
( 2 )( ) 72
x y xy
xy x y y x

  

  


6) Thay
yxb
x
y
y
x
a  ,

(6)



yxb
xy
a  ,
11

(7)







xyyx
x
y
y
x
yx
4)(
18
28) Thay
y
x
byxa  ,

18















32233
72
181
11
)1(
yyxxyyx
yy
xx


- ta thu
t 
  .
- 
22
7

11
,a x b y
xy
   

(2)
22
22
11
7
11
21
xy
xy
xy
xy

   




   



3) Thay
1
,
x


   


5) Thay
22
2 , 2a x x b y x   

19
(5)
22
4 4 2 2
47
4 ( ) 21
x y x
x y x x y
  


   




3. 







4
5
)1(
4
5
24
232
xxyyx
xyxyyxyx

2008).
6. 







.1
1
23
2234
xyxyx
yxyxx

7. 










.41)24()24(
29
yyyxx
yxyx

10. 







yyxx
yyxyx
)2)(1(
4)(1
2
2

.
11. 



20
3. 







.67545
125)13(9
22
33
yxyx
xy


2.6.   
Tro
.
2.6.1. 
2.6.2.   f(u)=f(v)
. 







2323
yxyx
yyyxxx
(
A 2012).

- 
f(u) f(v). 
(a;b) u = x - y, v = xy

- 
12,12  yvxu

 
2;2, vu









.
2
1
221812818128
22
2323