DẠNG 1: PHƯƠNG PHÁP RÚT – THẾ
1)

x2 y

2(x 2

xy

x

y)

y

2)

xy

2

y

y

x2

2xy

y

x4

4x 2 y

x 2 (x 2
xy2

2xy

2

y

HD : PT(2)

5)

x(2x
x2

HD : PT(2)
PT(1)

(x

x2
xy

6)

y

x

y

5

xy

x

y

xy
2

xy

x
x

HD : PT(1)

1

y4

; PT(1)

2

2

3y2

x

x
x

2)

1

y

x

5
2

5

5
2

2

5
2

)

;

5

1
1

2

29 1
;

29
2

(1)
(1;2),(2;1)

(y2

3y

2)(y 2

6y

11)

0

(1)

1
; PT(2)
1

(y2

y(x

4

3)

y)(y2

4y

( 1; 0),(0;1)

5)

0

(1)

(1; 0),( 1; 2)

(2)
1)(x

y

4)

0
(1)

2

( 1;

(2)
3y 1
; PT(2)
y 1

(y

2

2y

1)( 2y

-1-

(1
2

y

1)

0

)

)

0

3y
2y

2

1
(

(2)

y2

1

;

(2)

1

(x

(

0

5

(1; 3),(2;1)

2

1)

2y

1

5

(1)

1

3x(y
xy

(2)

y
; PT(1)
1

y
y

5;

(

(2)

y

( 3

2)

0
(1)

8

5
y

x
x

2)

9
x

2 2 ;1

(0; 0),(1;2),(2;2)

14

x

HD : PT(1)
9)

5y
2y

y2

y2

x

y2

7)( x

HD : PT(1)

8)

0

9

( 3

(2)

0

x

x2

x2

1

3y

2

HD : PT(2)
7)

5y

3y

0

0

0

5y

1)

3 2 ;1

(1)

x

3y)(x
x

1)

0
y2

x

21)

1

x2 x
2x 1
3x 2)(4x 2

y

x2 y

x

6y

(2)
3y
y
2y

1)(y2

2)(3y

2

(1)

0

3x 2

HD : PT(1)

4)

1

(1;2),( 4

(y

0

y2

(y2

PT(2)

3x

3y
x

3)

y
; PT(1)
1

2y2

HD : PT(2)
PT(1)

(2)
5
y

x

2xy

(1)

5

HD : PT(2)
x2

8

1
),(2;1)
2
2 ;1
2)

)

2 2)

TRƯỜNG THPT HAI BÀ TRƯNG

10)

x2
x

y2

xy
y

x
x

y

3(x
x

3
y

xy

y

x
x

3
; PT(2)
1

2x

3y

3x 2

y2

x2
x

y

x2

2y2

HD : PT(1)
x3
x

2

x2

y

2

x

2
y

1

x2
y

2

2xy

0

(0; 3),(3; 0)

2

3x)(x

0

2

5x

8)

0

(2)
(3y

2

8y

4)(y

1)

5
3 2
(2;1),( ;2),( ; )
2
2 3

0

(1;1),(

23y2

; PT(2)

y
; PT(2)
1
2

0

(2)

1; PT(2)

9x 2

2xy

0

0

2y)(y 2

3y

5)

0

x

(1;1);(

7x

2

x

y

1

(1)
3; PT(1)

(x 2

x)(x 2

x

6)

0

(0; 3);( 1; 5)

(1)

1

(2)
y

12
) (45x 2
3

36x)

3
4

4
;
5

(

6x 2 x 1
3x 1

2y

2 13
;
)
9
9

0

(2)
2

x

2x

59

31 59
; )
23 23

(2; 0),(0;2)

(y2

3

2x

82y

(1)
2y

y

(3;2),( 7 ; 3)

(1)

2x

y

y2

6)

(2)

3x

x

(x

y

(1)

0

HD : C1 : PT(1)
PT(2)

xy

2

4

y)x 2

y2

3y

y2

3xy

21)(y

(2)

2

(6

6x 2

4y

0

4
5

y

HD : PT(2)

(2; 3),( 3; 7)
2

(1)

x

2x

1

(x

3y 1
; PT(2)
y

2y

xy

2

(2)

5

xy

(y

6

10y

x

( 3;1),(1; 3)

0

(1)

3y

4x

HD : PT(2)

19)

y
; PT(2)
1

x

xy

9

(2)

y2

15)

18)

28

x2

HD : PT(1)

17)

y)
11
y

13)

6y

(1)

y

HD : PT(1)

16)

11

x

13) (CD

3y 2

2; PT(1)

xy

HD : PT(1)

14)

y

xy
2

HD : PT(1)

12)

(2)

x

y
2

(1)

2

HD : PT(2)

11)

13

3
);(0;1)
5

0

(1)
(2)

(

3

4 3 3 5 3
;
)
3
3

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

-2-

HD : PT(2)
(3y2

PT(2)
20)

3x 3
x

x

y)x 2

(5

2

x

C1 : PT(2)

4

y

x2

21) (B

x
2x

y

x4

2x 3 y

x 2 y2

x

2xy

xy)2

0

3)

2)(3x

2

0
(1)

2x

0

1)

6x

0

2x

9

(1)

6

(2)
( 4;

9

(x 2 4x)(x 2 8x 16) 0
6x 6
x
xy
2
2
x
6x 6
C2 : (2)
y
;(1) (x 2 4x)(x 2 8x 16)
2x
xy x 1 7y
(1)
22) (B 09)
2 2
2
xy
xy 1 13y
(2)
C1 :

x2

2

7y 1
HD : PT(1)
x
y 1
2
PT(2) (3y
4y 1)(12y2
23)

x2

2xy

xy

y2

24)

1

3x
2

3x y

2xy

4

2

x

y

5x

HD : PT(1)

y

26)

3x 3
x

y

x

C1 : PT(2)
PT(2)

(x2

C2 : PT(1)

y

y2 )x 2
y
y

2

2

0

2x)( x 2
x(x

(2)

2)(3x

2 2 ;1

( 3

5;

2)

1

5
2

(0; 0);(1;1)

0

0

(2)

2)

(0; 0),(2;2),(1;2)

0

0

(1)

3
x

( 3

(1)

2

2xy2
2

1
(1; );(3;1)
3

0

0

2

0

(1)

2

x2 x
2x 1
1)(x 2 3x

(6

2

(2)

3x
1
x 4)

y

3x

x 2 (2x 2

PT(2)

(1)

0

2

x

4x y

0

17
)
4

0

2

x
HD : PT(1)
y
x
PT(2)
x 2 (x 1)2 (x 2
25)

1)

0

2

x2

5y

3y 1
y
2
1)(y
y 1)

2y

xy

4

3x
y

x

(y2

x2
x

2y2
3y

HD : PT(2)
PT(1)

(0; 4);( 2; 10)

4

x(x

08)

(x 2

2x

2)

(2)

2x)(x 2

C2 : PT(1)

2y

2xy

y

(x 2

PT(1)

y2 4
2y 2
6y 22)( y2

(2)
x

3

4x
y2 )

3)

0
0

-3-

HPTVN

)

TRƯỜNG THPT HAI BÀ TRƯNG

27)

x2

2xy

2y

15

2x

2xy

y2

5

28)

xy
x

2

2y

16

2

2x

4y

x2

xy
2

y)
yx

2x

2

y

C2 : PT(1)

y

y2

HD : PT(2)

32)

x

33)

x2
x

2x

HD : PT(2)

y

34)

(2x

2x 2 y
7y

HD : PT(2)
PT(1)

(2x 2

15y

0

0

(1)

7

x
; PT(2)
1

y(2x

4)(4x

8y

32)

0

4x 2

(1;1)
2

(x

1) ( x

2)

1)

2)

0

(
4)

(1)
(2)
6
9x

20

6 7
37

;

26

2 7
9

)

0

9y

9x
7
2)(2x 2

x

(2)

9x
2x 2

2

(1)

2

x2 x 2
(2x 1)2
1)(37x 2 40x

3x

1)2 (5y2

(y

(2)

2y

y

( 4; 1)

(2)
10
; PT(1)
2

3
)
2

(1)

3
x

2x 2

(1;1);(2;

(1)

3

3xy
6

2y

(1;2);( 2;5)

2

10
2y2
y

(xy
2

PT(1)

3

2

x

xy

3

0

1)

y)

y

4

2

3)

0

5
1 0
(2)
x2
3 x
y
; PT(2)
2x 2 6x 4 0
x
x2 x 3
; PT(2)
2x 2 6x 4 0
x

xy2

HD : PT(1)

y

5)

y

xy

x2 y

3; 2

(2)
4y

2y)x
y

x

y

2

y2

2(x

2y)

55)

y)2

(x
x

y(x

( 3

(1)

7y

2

3)(x

09)

x2

3 2)

0

(2)

4y

1

(2y

C1 : PT(1)

31)

33

2

x(x
30) (D

2 2 ;1

(1)

1

x2

HD : PT(1)
y(x

35)

2y 16
y 3
4y 1)(y2 14y

y2

y(x

6x

(1

x

(y2

PT(2)

(2)

3x

HD : PT(1)

29)

0

(x 2

y

PT(2)

(1)

x 2 15
y
2x 2
2x 7)( 3x 2

HD : PT(1)
PT(2)

0

27)

1 1
16
( ; );( 2;
)
2 7
7
9 3 33
(
; 3)
4

0

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

-4-

35)

x2

x

x4

4xy2

y

5xy

(1)

4y2

12x 2 y2

(2)

x2 x
HD : PT(1)
y
5x 1
PT(2)
x 2 (x 2 3x 2)(13x 2
36)

xy

x

y

x3

4x 2

37)

xy
x 2 y2

3y

2xy

HD : PT(1)

38)

x3
3x

PT(1)

2x

y
y

39)

2x 3

y(x

4

6

5x

4x

(2)

y

40)

x

2x)(3x

2

5x

HD : PT(2)
PT(1)
41)

(x2

3x

12x

3xy

y2

y2

2xy

5

(2x2

y)(x

x(4x

1)

HD :PT(2)
PT(1)

(x 2

y)

8)

1
x
2

1)(7x 2

(x

12x

8)

14x

22)

(1; 3),( 3;15)
( 1

9
2x

6)

7;6

3 7)

0

(1)
5

(2; 1),( 2;1)

(y2

; PT(1)

x(2x

1)

7

1)(y 2

2y

25)

(2)

2

x

7

3
1)( 8x 2

4x

28)

0

(1)

3y
4x

0

0

(2)
2

2 23 153 44 23
;
)
7
49

1 1
(0; 0),(1;1),( ; )
2 2

(1)

11

6

(1)

(2)
5x

y)

y

)

(1;2)

(

0

2y

7

4

0

0

18

3)( x 2

y

x

4)

(2)

x2

x2

6y

2

2

9

2x

2) (6y

2

(2)

2x

y

HD : PT(2)

42)

y

17

(1)

2x 3 4x 2
HD : PT (1)
y
x 1
3
1
4
2
PT(2)
x (x
x
)( 4x 2
2
2

(x2

17 1
;

(1;2)
2

(y

x3 7
; PT(2)
2x 5
1) 4x 2

y

2

2)

(1)

3
2

2;

0

3y2

3

(

(2)

7

1)(7x

C2 : PT(1)

4)

3y 2
; PT(2)
y 2

5y

(x

y

1
(

2
1
x

4

x

C1 : PT(2)

5y2

2

2xy
2

2y 3

18

x
x
2)2 (x 2

2x

0
(1)

y

(x 2

PT(2)

2)

2
x

HD : PT(1)

9x

2
1
(0; 0),(2; ),(1; )
3
2

0

-5-

1
(

4

17 3
;

17
4

)

TRƯỜNG THPT HAI BÀ TRƯNG

43)

x3

7y

3x2

y2

8y

HD : PT(2)
PT(1)

44)

4

(x

xy

2x y

y2
5)

45)

xy

2

2

x

y

(1)

y(x

2

1)

12y

46)

xy
2

xy

x

10y

HD : PT(1)

47)

x2

xy

(x

y)(4

x

2

PT(1)

x

1

x2

HD : PT(2)

y

1

50)

16x2 y2
4xy

17y2
2x

HD : PT(2)

51)

x2
x

7y

4

2)

(x

y)(4

xy)

; PT(4)

x(y

4y2

20

16

2)

9y(x

3(x
2

y)

(3)

32

(4)

(0; 8),(2;2),(2; 6)

0

(1)
(2)

1

(y

3x 2

1)

( 1; 1)

4y
1)2 (36y 2

4x

1

60y

80)

0

(1)
(2)

x2

1
x

; PT(1)

2x(x

1

(1)

1

(2)

7y 1
2y 1
5y 1)(32y2

3xy

0

0

1)2 (x

y)
5x

9y

0
2

1)

(1; 1),( 2;

2)

5
)
2

0

1 1
(1;1),( ; )
4 4

2x

(4y2

PT(2)

2

1)

y)(x

9
; PT(2)
1

y

xy

x

2)

(3; 1),(1; 1 / 3)

2

1)(x

49)

16

4y2

5y
3y

2;1)

( 2; 1)

y)(x

(x

16

1)y

1)

6y

32

y

x2

x2 (y

(2)

xy)

(2y

x

1

2

1
(0; ),(
3

0

(x

(1)

6(x

HD : PT(2)

xy; PT(2)

2y

x

(2)

(2)

1

2x

1)2

(x

1)

0

7y 1
y 1
4y 1)(13y2

x

HD : PT(3)
48)

2

(3y2

PT(2)

1

1

7y

2

5y

1

(1)

2y

y2

HD : PT(1)

2

0

2x

(3; 1),(3; 7)

8y.

2

2

1

(1)

0

6y 2
HD : PT(1)
x2
y 1
PT(2) (3y2 4y 1)(12y2
y2

4

(2)

3x 2

3)(x

6y
2

7x

8x

8x

1)

2

x2 y

4

y)(x

x2 (y
4

y)2

(x

0

(1)
0

(2)

1
(0; 0),(1; )
3

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

-6-

x2

HD : HPT

52)

x2

(x2

y2

(2x

3y

3x

3y)2

1

2x

y)y

1

3xy

3x2 y

(3)
5x 2

0

2y

(4)

(1)

2y

(2)

(2;1)

C1 :Rut the
C2 :PT(1)

53)

(2)

10x

(x

xy

30x

2

y

xy

2)(x

2y)

2

2

(1)

2xy

x

y

1

10x 2
HD : PT(1)
y
x 1
2
PT(2) (15x
8x 1)(2x 2
54)

x2
x

4xy

4

8x y

HD : PT(1)
55)

3

4x y

x2
(x

7x

y(x
2

1

y
1

21

y2

PT(2)

3x

6y
2

2x y

2

(0; 0),(1;1),(2;1)

2)(4x 2

2)

(1)
1

1)

0

(1)
y

0

(0;1),( 1;2)

(2)

y); PT(2)

(x

y

1)2

0

(1)
10x

(2)

4y

12)

(5

2 2 ;2

2

(1)

y(x

2

1)

6y 2
y 1
3
1
y
)(36y2
4
3

12y

2

1

(2)
1
(0; ),(
3

15y

3)

0

(1)

y

8

(2)

y

x2

2xy

x4

4x2 y

8

x

3x; PT(1)

y

3x2

2 2)

0

16

HD :PT(2)

0
1
(1; 1),( 1; 3),( ; 3)
3

(2)

x2

(y2

x3y

2x

5y 2
x
y 2
4y 4)( y2
1)

3x

5x
2x

y(x

4y

xy

1

2)

x2

2

4x 2 (x 2

0

2

(y2

(2)

x2 y

y

xy

HD : PT(1)

60)

2

5y

4

0

1)(yx2

x2

x2 (y

2

1)2

2x

PT(2)

59)

x
; PT(2)
2

y)

0
(1)

2

2x

1)(x

HD : PT(1)

58)

2

1)

1
1
1
(1; 4),( ; 0),( ;2),( ;1)
5
2
3

0
4y

(x

(2)

3x

2

x
4x

(x

HD : PT(1)

57)

3x

1)x 2

(xy

2y

y

HD : PT(1)

56)

x

2

0

0
y2

(x

2

(2;2)

2) ( 3x

2

4x

(1)
0

(2)

-7-

4)

0

2 ;1)

TRƯỜNG THPT HAI BÀ TRƯNG

x2 x
; PT(2)
2x 1
y
; b 2y 1
x

C1 :PT(1)
C2 :a

61)

x

y2

4xy

y4

8xy2

C1 :PT(1)
C2 :a

62)

y2 x

HD :PT(2)
(y2

x

9x

HD : PT(2)

64)

10x
30x

x

PT(1)

67)

x2
x

3

8y2
2xy

HD : PT(1)

8xy
2

3)

3

13
2

3

17
2

;
;

11

3 13
2

10

3 17
2

)
)

0

2y

(1)

1)

(2)

2

( 3; 1)
(

3x
49x

4 78
;
13

78
)
13

0
49
y

2

(1)

8y

17

(2)
( 1; 4)

49

24xy)

0

(x

2y)(x 2

(1)

12y

12

;1

1
(1; 4),( ; 0)
5

49

12
2

(2)

1)

3xy2

2

x

2

0

1

5x

x2
3
24)

1)(2x 2

(x

1)

y

3(y

x3
x

(
(

3x

y3

3

y2

HD : PT(1)

(1)

3

x

xy

66) (HSG QG 2004)

3

(1)

2

x(x 2

PT(1)

1

0

1

8x

2

y2

HD : PT(2)

( 1; 1)

2

x3

0

(2)

2xy

A06)

2)

(

4)

10x 2
HD : PT(1)
y
x 1
2
PT(2) (5x
6x 1)(6x 2
65) (DB

2)(4y2

2

3xy

y

xy

y

9x
2
2)( x 2

2

3y

(2)

x2

3x

xy
2

y2 (y2

3

y

(x 2

PT(1)

(0; 0),( 1;1),( 1;2)

(1)

y2
2)(4y2

2y

(0; 0),(1;2),(2;2)

0

1

2y2

y)x 2

(9

2

4x

2y

2)

0

y2 y
; PT(2)
1 2y

x

3x 3

3y2

1
2
y
2y2
2

x

2)(4x 2

3x

0

4x2

2x
;b
y

2x 2

PT(1)

2x

2x

y

y

63)

y

x 2 (x 2

x

2

0

(2)
2

8y ; PT(2)

(2; 1),( 2;1)

xy

4y2 )

0

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

-8-

68)

x3

4y

1

2

y

y3
5(1

HD : HP(2)

x

3y2

3xy

x

y

2

y3

2

x

y(x

1

3y

1

4x

3y

The 4

3y

2

2

4x y

4x 2

2x

x2

y

2

xy
x2

y2

3

3

y

x3
4x 4

y3

6y x

5y

3)

3

0

(1)
(2)

3
)
y2

(1; 1)

(3)

3)

(1)

3

(2)

(x

2y)(x

2

2

2xy

4y )

( 2; 1)

0

(1)
2

(2)

2y 3
xy

2

2.7

(3)

2

(4)
(2x

y)(x

( 1; 2),(2;1)

2y)(x

y)

0

xy

1

(1)

x

3y

(2)

xy2

A06)

0

( 1; 1)
2

3

4x

2y (y

x)2

x2 )

(0; 0)

0

1

(1)

(0;1),(1; 0),(1;1)

y

(2)

(

HD :Thay(1) vao(2)
76) (DB

yx

y)(2xy

y2

y4

x3

(4)

HD :Thay(1) vao(2)

75)

x 2y

y)
2

y)(4xy2

1)(4x

(x

y)
2

x

4(2x

7

2x 3

xy 2

3 1
3 1
; ),( ; )
5 5
2 2

(1)

HD :Thay(4) vao(3)
74)

2y 3

(

3
y2

1

y3

xy(x

HPT

y2 ; PT(1)

(2xy

HD :The(2) vao(1)

73)

(1)

0

(2x

xy

x3

x2

y3 )

2

9y 3

0

(2)

5y)

2xy

4y)

(2)

9y 3

9

y)(7x

0

3y vao PT(3)

16x 3

2x 3

y

2

2

x(3x

4

y)(x
2

0

2y

2(x 3

16x 3 y 3

(0; 2),(1; 3),( 1; 3)

4

20y 3

HD : PT(1)

72)

5x

2

y3

x3

71)

2

4x)

2

x

(2)

x)

4(y

HD : PT(2)

70)

(1)

2

x3

PT(1)
69)

y

16x

xy(x

x3

8x

x2

3

HD :Nhan cheo ve voi ve

2

4xy

y3
3y2
2x(x

2

3y )

0

3
3

25

;

3
3

25

)

2y

(1)

(3;1),( 3; 1)

3

(2)

(

3y)(x

4y)

0

-9-

4 78
;
13

78
)
13

TRƯỜNG THPT HAI BÀ TRƯNG

77) (DB

B06)

(x

y)(x2

y2 )

13

(1)

(x

y)(x2

y2 )

25

(2)

(3;2),( 2; 3)

HD :Nhan cheo ve voi ve
78)

(6

x)(x2

(3

2

y)(x

y2 )

6x

8y

2

8x

6y

y)

HD :Nhan cheo ve voi ve
79)

2y(x2

y2 )

x(x2

y2 )

(x

(1)
(0; 0),(2;1),(4;2)

(2)

2

2

y )(x

2y)(4x

3x

(1)

10y

(2)

2y

15)

0

(0; 0),( 2, 1)

HD : Nhan cheo ve theo ve

80) (DB

27x 3 y 3

D10)

9x2 y

27x 3 y 3

PT(1)
81) (DB

1)3

xy(5y

8

42xy

63x 2 y2

(

2
1
; 2),( ;1)
3
3

(

1
1
; 3),(
;
2
2

0

2

9x

9

(1)

0

(2)

3xy2

9x

(3)

6x 2 y

(4)

5xy)

3
),(1; 3)
2

(1;1)

(1)

3y

(2)

1 3y
5y 1
1)( 375y2

1
;b
y

xy

5) x 2

2y

3y

x2

x

y

1

y

2(x

x2

135)

2y( x 2

3

0

2y)
(

6

3y; PT(1)

5
2

3) x

1

x2

HD :PT(1)

y

PT(2)

3)(x

(x

50y

6

HD : PT(2)

84)

7y 3

xy

x

2

y2

1

y 3 (y

(x2

3y

6x 2 y

2y3 (9

1)

C1 : PT(2)

C2 :a

y

9x

(xy

x

6x y

(2)

42xy
2

3 15
)
2

(1)

42xy

6xy

2

4x 3 y2

HD :HPT

83)

4x y

B10)

PT(1)

7y 3
2

8

6x

63x 2 y2
2

82)

y2

63x 2 y2

HD :PT(2)

7y 3

5 15
,
2

(

5x
2)

(1

5y) 6

3
4
21
4
2(x

5y

5y

9

(3;

3) x

1

3 ;1)

3
)
4

0

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

- 10 -

x

85)

x

y2

x

y

y

2y

4

4

3x

6

x2

xy

x

(x

1)2

3(y

2

2

x

88)

1

x( y

89)

x2 y

90)

x2

91)

1)

2

6xy

0

6y(y

1)

7 y

1

1
1
x
5x

xy

3
1

x2

y2

2 x 2 y2

x2

5

2y

3

y

3

x4

x3
1

HD : PT(2)

x

y

y(2x2

0

(2)
x)

12

(2)
(1;

12)

2)

9
),(3; 0)
8

0

(3; 3),(

xy

2

y2

y)

14

2

3)

(0; 3),( 2;1),( 4; 1)

(y

3)( 2y

2

1) ; PT(1)

3;

0

y2

; PT(2)

x

1

2

y2

y)

0

(1)
(2)

(x

2 ;2

(1)

y
y

(1;1),(2

0

(2)

3

y

(2)
( 1; 3)

4

y2

xy xy2

0

(1)

x2

y

2y)

1

x2

y2

y2

x

(1)

13y

4x

3

4

0

1

(x 2

xy2

x

2

3x

1

2

(2; 1)

0

y2

y

HD : PT(1)
92)

x

x
1
7
3)(x 2

x2

HPT

x2

1

2x 2

HD : PT(1)
PT(2)

y

0

x y

6

x2y

3y2

1

(1)

3

y

6y2

HD : PT(1)

1

x

x2

3y
2y

y

(1)
x

2

0

(2)

2(xy

2.

1)(

x

2

x2

2

y
x

1)

y
x2

(y x)2

0

xy

3.

(3

2
4 x

3

x)2

(y

0

3x

x

PT(2)

2)

1

PT(1)

(4;2)

; PT(2)

y

y

HD : PT(1)

2

2x

A05)

0

2
5y

2)( y2

HD : PT(2)

87)

y2 x

x

y

86) (DB

1

2y x

HD : PT(1)
(y2

1

(6x

2

5x

(1; 0)

1)

- 11 -

0

TRƯỜNG THPT HAI BÀ TRƯNG

x

3

93) (B

02)

x

HD : PT(1)
94)

y

x

y

3

x

y

x

y

6x 2
3x

y

98)

2
y)3

(x

(x

y2

2

(2)

1) 3(x

y

2y

1)(3x
x

x3 )

1)

y

1)

0

3

1)3

6x(x
1)2

3y(x

(1)

y

x

1

y x

(2)

1

HD : PT(1)
100) (A

y
y

4x

14)

HD : PT(1)

(x

(y

x 12
x3
x

1
1

0; PT(2)

y2 )

y

1
(0;1),( ; 0)
3

(2)

x(y

2

4y 3

4y x

x3

0

1)

y2

y

y)

y

8x

1

12

y

0

(2)

(y

1)

14 5
; )
9 18

0

2

1) (y

2

3)

4 3;

3)

0

(1)
(2)

y2 )

(

(0; 1),(7

2)2

3
1)(x

(2 3 4 ; 3 4)

(1)

1

y)(x

x

2

2x

(x

y)2 (1

0

1)2

3y(x

x

0

0

3) x
y

2y

2(x

y)

(1)

(x

2y)(x
3

x

2y

y)

(x

y)2 (1

(2)

3x

(y

HD : PT(1)

99)

(x

(1)

xy

HD : PT(2)

y)3

1

2y2

2(2y 3

(2)

y

x2

x2

2

x

(2x

3 1
(1;1),( ; )
2 2

(1)

(1)

y)2

3xy

y

(x

x

HD : PT(2)
97)

y)2

(x

y

x

3

HD : PT(1)
96)

x

y

(x

HD : PT(1)

95)

y

(2;1)

0

y(12

x2 )

2 y

2

12

(1)
(2)

(3; 3)

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

- 12 -

DẠNG 2: PHƯƠNG PHÁP CỘNG
101)

x2
3x

y2
2

2y

HD : 3.(1)

102)

5x

16x

(3x

2x

4y

y

1.(2)

x2
x

2

2xy
(2)

7x

x

1

1)2

x2

(2y

x2

(2x

9

y

5)

2)

3

(1)

3)(2x

1

y2

2x

y

1)y

1)2

2

(

2)

5

3 2)

6y

3x

2)

2)(2x

13)(x

2y

2

3)

0

(1)

1)

3y

13

(1)

3y2

2xy

2x

11

(2)
9y

4x2

3y(x

1)

7

(1)

3y2

4x(y

1)

3

(2)

HD : 8.(1)

3.(2)

3y

5)(2x

2y

13)(4x

3y

x2

2

x(y

1)

(1)

y2

7

y(x

1)

(2)
2y

4)(x

y

( 3;1);(0; 2)

0

3xy

(8x

( 1; 1)

0

(2)
2y

11 12
; )
5 5

(1)

0

y

(8x

( 1; 0);(

0

20

3y

1
;1);( 1; 0)
2

(2)

y

4y2

2y

(x

3 2 ;3

0

(2)

(3x

4xy

y

(1)

3)(2x

2y2

2.(2)

(2

0

(2; 1);(1;1)

2x2

HD : 1.(1)

0

28 24
;
)
29 29

0

9.(2)

111)

(

4)

HD : 8.(1)

110)

(2)

(2)

y

2xy

(x

y

0

2y

6(x

y2

HD :PT(1)

5y

y

4xy

13

(1)

(2x

2x2

3

; 0)

(1)

(2)

4.(2)

(x

13)(x

2x

xy

(2)

y

y

y2

2

(2)

3)(x

2xy

0
6y

33

y

2y2

16

8)(x

(2x

1)2

3x2

8y

13

; 4)
2
(4; 0);(0; 4)

0

3

(2x

x2

(

3

(1)

(x

y2

xy

(

(2)

2y

16

1.(2)

109)

4xy

2y

HD : 2.(1)

108)

x)

2

HD :(1)

107)

4)(4

3x

x

3
20y

2

HD : 1.(1)

106)

2

(1)

8y

xy

HD :(1)

105)

1

5y2

5.(2)

HD : 2.(1)

104)

9x

(4x

2

HD : 7.(1)

103)

4y

1.(2)

y2
y

3x
2

3)

1)

5)

7
( 4; 3);( 2; )
3
17
( ; 7)
2

0

0

5
(1; 2);(1; )
4
19
(4;
)
3
(

0

- 13 -

1
;
2

7
)
2

TRƯỜNG THPT HAI BÀ TRƯNG

112)

x2

2xy

xy

2

HD : 1.(1)

y

2y2

3x

3y

.(2)

1

0

(1)

0

(x

(2)

2y

1)(x

2y

2)

0

1
5
113) (HSG Nghe An)
57
2
4x
3x
y(3x 1)
25
HD :25.(1) 50.(2)
(15x 5y 7)(15x 5y 17)
x2

114)

2x 2
x2

y2

3xy

HD : 8.(1)

9x

2y2

xy

y2

3x

15.(2)

(x

6y

6

12y

10

2y

0

6)(x

y2

xy

(1)
(2)

11y

x

33)

7y

115) (HSG Dien Bien) x
x 12
y
HD : 4.(1) 1.(2)
(x 4y)(x y

116)

2xy

3y2

2x

10y

y2

2y

0

2x2

2xy

HD : 2.(1)

9.(2)

(8x

y2

xy

2y

x

2y

2

0

(x

y

117)

x2
2x

2

y

2

HD : 1.(1)

3.(2)

118) (DB

A05)

HD : 1.(1)

2.(2)

119)

2x2
2y

2

y2

8

2

120)

x

2xy

HD : 1.(1)

1.(2)

121)

x2

y2

x2

2xy

2x2

x(y

122)

x2

HD :3.(1)

xy
4.(2)

y

2x

4)

1)

0
( 2; 4),( 2;2)

(

12 3
; ),(3;1)
5 5

(0; 0),( 2; 4)

0

1)

2

4 7 7 5 7
;
)
7
7

(1)

(1; 2),( 2;1)

(2)

(

2;

2)

(1;2)

3y

2x

3

17

0

5)

5

2)(y

2 1 11 2
( ; ),( ; )
5 5 25 25

(

0

4

1)(9x

y

(y

4y

(2)

2x

)

(

7y

1

2

(2)

(1)

y

5

(1)

y)

3

2xy

y2

7x

1.(2)

y)(x

(3x

xy

HD :1.(1)

y(y

x

2y

3x 2

1)

x

7.(2)

2y2

y

1

3 17 34 8 17
;
)
17
17
( 1; 2),(1; 0)

1)(5x

y

5;

2)

0

(1)

2)(2x

x

(x

4)

0

y2

x(x

3y

HD : 17.(1)

x2

x2

(2)

2

( 3

(1)

(2)

3y

(2)

2 2 ;1

0

2

x2

(1)

( 3

0

(1)

( 1; 0)

(2)

(

3)

0

11 12
; )
5 5

(1)
5y

(y

9

2x

3)(y

1)

y2

3y2

x

2y

(10x

9y

(1;1);(2; 1)

(2)
x

2)

0

3y

(1)
(2)
1)(x

y)

(0; 0)(1;1)( 1;1)(

0

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

7 3
; )
43 43

- 14 -

123) (DB

C1 : 3.(1)
C2 : PT(1)

124)

y)

(1)

x2

xy

y2

7(x

y)2

(2)

(x

y

y)2

x4

2x2 y

x2

y2

(x 2

4x 2

y2

2

2

2y

x2
x

2

xy

y2

xy

2

y

2x2
y2

9

22

0

2xy

9(x

y

y

y)(x

0

3)

y

1)

0

0

(1)
(2)
2

4y

y

27)

5)

0

y)2

2 ;5)

(1)
(2)

y)

(x

y)2

21(x

y)

0

5

( 2; 3),(

0

y)

7(x

5x

1.(2)

0

7)(x

7(x

y)2

xy

C1 : 1.(1)

6y

19(x

xy

21(x

y)

2)(x 2

y

(x
y
22 2y
x2
y 1
8y 15)(y2

HD : PT(2)
PT(1)

y)

2

2.(2)

(y2

PT(1)

3(x

(0; 0),(1;2),( 2; 1)

0

3

x4

x

y)2

y)

3

(2)

xy

1)(x

9(x

y

C2 : PT(2)

127)

3(x

(x

9(x

C1 : 1.(1)

126)

y2

xy

HD : PT(1)

125)

xy

D06)

1.(2)

PT(2)

x2

(0; 0),( 2; 3),(3;2)

21(x

y)(x

y

1)

0

(1)

7

(2)

(2x

y

( 1; 3),(1;1)

1)(x

y

2)

0

C2 : Rut the

128)

x4

4x2

x2 y

C1 : 1.(1)

2x2

129)

5x 2

3x

2xy

2y

2xy

5y2

x4

1.(1)

y2

2

xy

2x

C2 : 1.(1)

(2)
12)(x 2

y

4)

0

(y2

17)

3x

2y

0

(1)

(1; 0),(0;1)

3x

3y

2

(2)

4 6 5
( ; ),( ;
7 7 7

3
)
7

( 3;2),(

3 ; 8)

(2x

8x2

6y

y

38

y

2)(2x

1

0

y

1)

0

(1)
(2)

38 y
y 2
10y 16)(y2

2.(2)

(x

2

( 1; 3),(1; 3)

8y

x2

C1 : PT(2)
PT(1)

2

(1)

23

2

HD : 3.(1)

130)

6y

2

(x 2 y
23 6y
x2
y 2
8y 15)(y2

(y2
2

4y

2.(2)

C2 : PT(2)
PT(1)

y2

y

8y
11)(x

52)
2

y

0
7)

0

- 15 -

TRƯỜNG THPT HAI BÀ TRƯNG

131)

x4

2x2 y

x2

y2

C1 : 1.(1)

y
x2
y

y3

2y

x

(2)

y

3)

0

y2

y

(2)

(x

2

y)(x
x2
y

03)

y

xy

3)

(0; 0)

0

2

(1)
(1;1)

2

(2)

x2
y)(3xy

(x

2

2

y2

3y
HD : (1)

(2)

x2

3y

2

0

(1)

y2

3x

2

0

(2)

HD : (1)

134)

x

y

y)

3)

0

(1;1),(2;2)

(2)

(x

y)(x

x

2

xy

x

2y

(1)

y

2

xy

y

2x

(2)

HD : (1)

(2)

(x

y)(x

2x

y

135)

y

0

1)

(1)

x2
3

(1;1)

2y

x

HD : (1)

(2)

y2
(x

4

y2

(1)

4

2

(2)

137)

x2 y
xy

2

HD : (1)

(2)

2x2

y

138)
2y

2

x

x

3 3
(0; 0),( ; )
2 2

0

3

136)

(2)
y)(2x 2

(x

y)(x

1
y
1
x
(x

2y 2 )

3xy

y

xy)

0

(2;2)

0

(1)
(1;1)

(2)

HD : (1)

(2)

x3

x2

x

1

2y

(1)

y3

y2

y

1

2x

(2)

139)

HD : (1)
140)

(x

y)(x

y)(x

y

2

xy

2xy)

y

2

0

x

y

x3

2x

y

(1)

3

2y

x

(2)

y

HD : (1)

141)

(2)

(2)

3 ; 1)

(1)

3x
133)(B

2)(x 2

y

3

2x

( 1;1),(

(2)

(x2

x3

HD : (1)

(1)
3

1.(2)

C2 : PT(2)
132)

3

(x

y)(x2

y2

xy

1)

3)

(1;1),( 1; 1)

0
(0; 0),( 1; 1),(

3;

3)

0

2x

3

4

y

4

(1)

2y

3

4

x

4

(2)

(3; 3),(

11 11
; )
9 9

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

- 16 -

142)

143)

x

1

y

7

4

(1)

y

1

x

7

4

(2)

x

1

y

2

3

(1)

y

1

x

2

3

(2)

x

3

2

y

3

(1)

y

3

2

x

3

(2)

144)

145)

2x 3
y

3x2 y

3

6xy

HD : 4.(1)
146)

y3

2

2y

HD : 1.(1)
147)

2x2

150)

y3

x2

2y2

8x 3 y3

152)

(x

4)3

4y

3)3

(y

x

y

5

(2)
y)3

(3

x

0

7

y

(2)

3

(x

1)

3

(y

2)

x

(1; 2),(2; 1)

y

3

18y 3

(1)

y2

(2)
18y 3

108xy

72x2 y2

108xy

(x

1) y

x) y

1

1.(2)

(x

1

27

y

0

6

(1)

4

(2)

y

1

2)(x

y

1

(0; 3),(1; 0)

5)

0

x

1(1

2y)

y

2

0

(1)

(2;1)

y(y

x

1)

x

4

0

(2)

19
(

( x

1

y)(2 x

y

0

HD : 3.(1)

153)

2)3

72x2 y2

(2

(2; 3),(3; 2)

(1)

6x

1)2

3

(2)

9y

27

HD :1.(1)

y

9y

16x

x

8x 3 y 3

x

x

9

HD : PT(2)

151)

2)

(1; 2),(2; 1)

(1)

3.(2)

(x

(y

91

x3

PT(1)

3

(1)

3.(2)

4x2 y

(2)

1)

(x

3y2

HD : 1.(1)

0
3

4x

y3

4x2

3

35

3.(2)

HD : 1.(1)
149)

4y
(x

3y2

x3

y)

3

(1)

x

y3

HD : 1.(1)

148)

(2x

3.(2)

x3

(1;1),( 2; 2)

(2)
3

9
2

(3; 3)

(1)

7

1.(2)

x3
x

5

2

(8; 8)

2.(2)

4x

y

4 (1

HD : 4.(1)
(8 1

3 1
x)(1

y)

6 1

1

2y

3)

0

(1)
x

1

0

(

(2)

3.(2)
x

2 1

y

3)(2 1

x

2 1

y

3)

- 17 -

0

3 13 3
13
;
)
8
4

3
; 0)
4

TRƯỜNG THPT HAI BÀ TRƯNG

154)

155)

x2

2

y2

3

x

y

5

(1)

x2

2

y2

3

x

y

2

(2)

x2

x

y

1

x

y2

x

y

1

y

18

x2

x

y

1

x

y2

x

y

1

y

2

(4; 4)

DẠNG 3: PHÂN TÍCH THÀNH PHƯƠNG TRÌNH TÍCH

156)

x2
3x

5x
3

xy

HD :PT(1)
PT(2)

y
2

(x

y
2

9
2xy

9
2x

(1)

x

6x
2

3)(x

2

18

(2)

5x
2

2x

6)

(1; 3),(3; 15)
( 1

17 ;

4

7 7)

0

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

- 18 -

157)

2x2

y2

xy

x2

y2

x

HD : PT(1)

158) (CD

y

(y

x

HD : PT(2)

C2 : PT(1)

y

PT(2)

1)(x 2

(x

2xy

3x

2

2

x

4y

HD : PT(1)

161)

x

6

2

HD : PT(1)

162)

x2

y2

HD : PT(1)
163)

(1;1),(

4x

12y

2x

4)

3)

0

2y
2

2)(y

3
3)

2y2

(2)

3x

3y

2y

2

(1)

0
(1)

4x(y

1)

3

(2)

1)(3y

x2

2y2

2xy

2x 2

y2

2y2
x2

4x

3)

15

0

y

x

y

4

(2x

y

1)(x

3x

(x

2x2

xy

3x2

2xy
(x

2y)(x

y2

2y

5)

2

0

7y
y)

3x

2)

y)(2x

y)

0

(1;1);(

0

;

1

11
4

0

0

4
;
5

)

13
)
5

(1)

(1; 1);(3; 3)

(2)

( 13

(1)
1

4

(1)

0

y

11

( 1; 2),(1; 1)
(1;2),(3;1)

(2)

3

3

0

0
y

(

5
19
( 2;1);( ;1),(4;
)
4
3

(1)

0

y2

0

(1; 3);( 2; 0)

0

0

y2

xy

1)

(2)

3)(x

5x

x2

2y

5

y2

xy

HD : PT(1)

4y

2y

xy

x2

2)(2x

(2)

7

8x

5)

(0; 3),(2;1),(2; 3)

0

1)

4y2

;

0

3y(x

(x

2

(1)

4y

x2

5

1
3
( 2; );(2;
)
2
2
7
3
( 2;
);( 6;
)
2
2

3

2)(2y

(y

1

0

2

3y

0

0

4x 2

HD : PT(1)

167)

y

y

HD : PT(1)

166)

1)

2xy

(x

HD : PT(1)

165)

y2

1)(2x 2

x

4xy

HD : PT(2)
164)

x

6

4xy

0

x

(x

2x 2

(2;1),( 2; 1)
(2; 3),( 3;2)

2y

1)

y

4y

4y

x

x2

y)(2x

3x

2x

0

4 13
;
)
5
5

0

x2 y

(x

xy

y

2

(1;1),(

7

2y)(x

2

1)

2

2y

2x 3

(1)
(2)

y2

x

0

2x

xy

xy
(x 2

160)

2)(y

2

C1 : PT(2)

2

0

xy

(x

12)

y

4

x

x2

14)

159) (D

5x

(2)

- 19 -

157;

13

157
2

1 1
( ; );(3; 3)
2 2
5
45 5
45
(
;
)
10
5

)

TRƯỜNG THPT HAI BÀ TRƯNG

2x2

168)

2xy

x2

(x

2x2
x

5xy

HD : PT(1)

x2

170)

x

2x

y

x

y

y

y

2

2x

y

11)

3)(2x

y

2

y

2

y2

2

4)(4

x)

y2

5x2

4xy

16x

5x

y

2

1)

0

2(x

y)

2

(x

y)2

y2

2)

0

8y

16

0

x

4)

0

4)(y

3y

(x

4
;
5

13
)
5

2
;1);(2; 3);
5
1 4
(
;
)
6 3
(1; 1)

0

3y 3

1)(x2

(y

1)
x

2x

(5x

(2)

0

1
(

y2

C1 :(1)

1)

4

y2 )

2y

y

2y

xy(x2

xy

0

1

4xy2

x2

( 1; 1)

(

5x2 y

x

(2)

8
(0;1);( 5; )
3

(1;1);(

x)(y

y2

0

1

2)(2x

xy

xy

5)

(1)

1)

(1)
(2)

0

2y

y)(x

(xy

HD : PT(2)

0

4

2x

x

15

3

(y

HD : PT(2)

176)

(x

(x

HD : PT (1)

175)

y

xy

0

5x

x

2x2 y

3

174) (A

2

18y

y

y

(2)

2

x

6x

HD : PT (2)
173)

3x

y)(x

2xy

2x 3

11x

2

2x y

xy

2

0

3y

xy

y2

1)

2

HD : PT (1)
172)

y)(2x

(x

2

2

0

xy

HD : PT (1)
171)

1

(x

3

(1)

x

2y

2y2

3

0

3y2

7xy

2

y

3y2

5xy

HD : PT(1)

169)

x

0

17
2

;10

17)

(1;1);( 1; 1)
(

2 10
;
5

10
)
5

(0; 4),(4; 0),(

4
; 0)
5

0

0
y)(x

y

1)

4y 3

0

0

2 1
(0; 0),(1;1),( ; )
3 3

C2 : Rut the

2x2

8xy2

xy

16x 3

2x

8y2

HD : PT(1)

(x

177)

178)

x2

5x
2

4x y

HD : PT(1)

5

0

4y2 )(2x

xy

3y

y)

0

6

3xy

2y

2

9

(x

3)(x

2

1
( ;1);
2
3
19 3
19
(
;
)
4
2
3 233
)
4
1 9
( 1;1);( ; )
4 4
( 3;

y)

0

45

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

- 20 -

179)

x3

3x2

3y

xy

9x 2

3x

y

C1 :PT(1)

(x

3)(x 2

1

y)

C1 :PT(2)

(y

3x)(2y

y2

xy
x

2

5y

2x
2

3x

HD : PT (1)

181) (A

x

2)(y

x

1
x

y

HD : PT (1)
182)

(x

8y

x

x3

x2 (y
(x2

HD : PT(2)

183)

3x

6(2x
184)

y3

x2 y

x

2

3y

186)

x

xy

2

x

187)

x3y

3

2

HD :PT(1)

188)

2(x
x2

y2

HD : PT(1)

(1)
(2)

y) . (3x

y)

2(3x

(y

x)(y

x)(y

2x)

0

1

5
2

321
8

1

;

5
2

)

1 1
3 9
( 1;1),( ; ),(
; )
2 4
2 4
1
209 15
209
(
;
)
8
8
1 2
(1;2),( ; )
5 5
3
11 9 3 11
(
;
)
12
4

3 23 3
( ; ),( ;
)
3
3
3
2 32
1

(1)
(2)

1)

3x

(

0

y
y

x 2 y2

2)

1)(x

y)

xy

(1; 1)

(1;1);( 1; 1)

(2)
1)

0

(1)

3

(2)
5xy

1
)
2

(1)

1

(xy

1
;
2

0

1
2

3

1

(1)
(2)

xy

8

1

;

0

y2 )

1)(x

2x 2

y)

(2)

2

x4

x

0

2

y)(xy

(x

xy

y)2

10(3x

(1)

2

2

HD :PT(1)

0

1

(x

321

0

x(1

2

HD :PT(1)
x2

2y

5(3x

y3

x2 )

y(1

15

;2)

0

1

2xy2

2

(

6

y)

HD :Thay(1) vao(2)
185)

(

17

(1;1)

2)

y2 )

y
y)

y)(9x

x3

y

3(9x 2

3x
(3x

HD : PT(1)

0

y2

xy

1

y

2)

1)

y)(x

y)2

(3x

0

4xy
2)

3

(

1

y)(xy

3

0

1
y

x3

2y

1)

22

(y

03)

0

0

2y

1 5 3
5 9 3 5
; ),(
;
)
2 4
2
2

(

3x

4

(3; 4),(3;9),( 1;2)

3

3xy

180)

2y2

x

2y2

0

(x

(2;1);( 2; 1)

2y)(2x

- 21 -

y)

0

)

TRƯỜNG THPT HAI BÀ TRƯNG

189) (CD
HD : PT(1)

190) (D

08)

1

2x

2y

1)

0

7x

4

0

(y

3)(y

x

2x 2

y2

3xy

4x 2

y2

x

4

1)(2x

y

(x

2xy2

y2
3

(y

(y

3)x

2

2
(y

1)(y

3

3)(x

y

0

1

2y

1

HD : PT (1)

x3

( x

6x2 y

x

y

HD : PT(1)

x

3
3y

5

x)(3 y
3)2

4(3y

6y

9)

1

6y

(3y

(x

2y

9(L) vi y

(2)

(0;1),(1;2)

1

(2)

8)

(3; 2),(3;2)

0

(1)

1)

(3;2)

0

2 y)

0

0

(1)

(2;2)

(2)

(32

8 15; 8

2 15)

0

1)

xy

(3y

x

x
x

x)(y

( y

1)(x

(1)

y)2

1)

2y

4y

0

2

2

(x

x

(2)

3(y

C2 : PT(1)

y

(1)

(2)

C1 : PT(1)
1

1)

0

8

4y 3

4y)(x

x

2

2x

1

y

2 (3y

1

(1)

9xy2

(x

(1;2);(4;5)

7x

y)( x

x

2y

3

y

xy

(1)

0

3x

2

4y

2y
x

1)

2x

x

(5;2)

(2)

x2

15
2

(2)

3

7y2

13

x

x

197)

y

0

2y

y)(x

3x

( 3;7);(1; 1)

(1)

(x

2)

3y2

1)

y x

x

y4

y

2y2

y(y

(1)
(2)

x2

6 y2

13)

y

y

3

HD : PT(1)

x

2

y

5y

HD : PT(1)

196)

2x

2

3)( 2x

x

x 2y

HD : PT(1)

195)

y

3

x2

192) (B

194)

y

2xy

xy

HD : PT(2)

193)

x

2

( 2x

HD : PT(1)

191)

2 2x

10)

(1)
2y

2

(2)

x)

2 (3y

1

3y
x)(y

x)

x)(y
0

1)

(3;2)

1)

0
2 / 3; x

3

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

- 22 -

198)

2

x
y

6y
x

x

HD : PT (1)

y
y

HD : PT (1)

200)

x2

x

x
(y

2 x2

205)

14)

4 x

207)

x
2y2

0

(1)

1)

y
y

16

2

x)

2x

14

x

2y)

(5;25)

(1

1

y2

x

y)

x)( x

y

x

x

2

3x

6y

1

2 x

y)( x

y

4y 3

2 3

2

y

4)

0

y

1) y

2y

4x

y

y

2)

0

5y

3

(1)

(3;1)

(2)

1
(

5
2

xy

y2

3)

3(x 2

2

16

3y

x2

8

1)3

(y

1)3

y2 )

2

(1)

(8; 4)

(2)

(8

(1)
(2)

x

y

;

1

5
2

0

3 3
;
3 3

0

y)(x2

2 x
2
y
1 3xy

1)

16y2

16xy

(1; 0),( 2; 3)

0

(x

1)( x

y

( x

2)

(1)
(2)

2y) (x

2; 1

0

y

2x)

(2)

(2)

y) x

y2

12

2

(1

y
x
2y

0

(1)

y3
2

1)

0

y

(x

y

(1)

( x

x

( 1;2)

(2)

0

1)(x2

y

(x

(1; 0)

0

y)( x

2 y

3

2y

x)(y

3y)

2xy

4x2

HD : PT(1)
(y

y

2) x

2x2

3x2 y

HD : PT(1)

1

1. x

2y2

HD : PT (1)

206)

y

y)(x

(1

x

(x

(y

2xy
x y
x2 y

C2 : PT(2)

HD : PT(1)

1)

4

(x

(x

x3

1)( x

1

y

204) (B

y2

xy

y2

C1 : PT(1)

x2

2

2y

x

1

2)(y

2

HD : PT (1)

203)

y

y

4

2y

x2

2y

8 4
(12; 2);( ; )
3 9

(1)

(1

HD : PT(1)

202)

2y)( x

y

2)y

3

(2)

(2)

(x2

x

2

5

HD : PT (2)

201)

3y

2y

( x

1(x

y2

(1)

1

y2

y

x

x

x

2y

2y
( x

x

199)

x

4)

(2; 0),( 1; 3)

2.

(1)
(2)
2x)y

2x x

(
0

0

- 23 -

2

2
2

;2

2)

)

TRƯỜNG THPT HAI BÀ TRƯNG

208)

2

6y

x(1

x

8y)

HD : PT(1)

x
y

2y

x

2

( x

(1)

2y
2y

(2)
3y)( x

12y
3 x 2 4y
209)
x
y 3 y x2 x
C1 : PT(1)

(3 4y

C2 : PT(2)

( y

2x(y
210)

x2

y

x

(4y

1) x 2

x4

x2 y

x2

213)

y2

4y2

2xy

2y

6 y2

y(y

x

2)

3x

x2

y

2x

x

215)
1
HD : PT(1)

2y

(x

y) x

( y

2)( x 2

2x 2

y

x

2)

1

1)

(1)

3)( x

4

2y

1

2)

0

x
y2
2 x

0

3)

0

4xy

13
x

1

(x

2

5)

(2)

y2

(1; 0)

0

y) x

y

0

0
(1)

0
1)( y

(1;2);(4;5)

(1)
1

2y

1
(1;1),(2; )
2

(1)
(2)

y

(0;1)

0

1)

7x

2y

)

(1)

(2)

1)(x

2

0

1

1)(2 x2

x

5

(2)

y

1

3

(1)

y

1)2

(x

xy
xy x 2

3

1)(y

4(y

y

0

3

xy 2y2
x y

HD : HPT

x)

7

3

214)

3

4(y

5y

2)2

1)( y

2y

x2

(x

0

(2)

2x

(2 x

(y

x)

2y

1

1

HD : PT(2)

(2)

1

2y

HD : PT(1)

3

x

1

( x2

x

(1)

2 x2

5 5;

0

x

1)

y

2y)

x

4

( x2

2y

x)( 4y
x

2y(y

HD : PT(1)

212)

3

1)

HD : PT(2)

211)

x

(11

(1;1)

(2)
x)

0

“ Các yếu tố của nghệ thuật học tập là ý chí, trật tự và thời gian”

- 24 -

216)

x2

2xy

x

2y

1

(2)

y)(x

(x2
x

y

2

218)

PT(2)
219)

x

1( x 2

1

x

220)

x2

2x

225)

2x
2x

y)

0

y

2

0

y

2)

3y 4

0

2y
(x

2x

y

2

)

(1;1)

(1;1)

1
(0;1),( ; 3)
2

0

2

y )(x

2xy(y

1)

0
2

y

3y )

4x 2

10x

18

y

y)(2x

y2

2y(y
y

5

2y)(3x

y

(1;2)

(2)

1

y

4x

29

(1)

y)

1)

2

29 3
;

0

(2)

1

y2

2)

(1)

0

4y2

7y

1

(2)

0

(2x

1
(

y)y

1)(2x

1

5

(2)

(1)

2x

y

0

( 3;5)

2y

2x)

6 2x

HD : PT(1)

3)( x

1)(y

x2

x

y

)

(1)

x

(x

1

(1)

1)

(y

5y

x(3x

1

3x

1

y

0

y

y3

HD : PT(1)

6)

y2

2y2

1

1

0

3xy
y)(x

(1;1),( 1;1)

(2)

9

y

(1)

1)( x 2

0

1)

2y

y2

2x x

(2)
y

4(y

y2

1

0

0

x

y)(x 2

(2x

HD : PT(1)

224)

2

1

2

2

2

y y

7

(x 2

8 1

x

2x

(x

HD : PT(2)
223)

1

2x 2

4xy

(x

7)(x

2xy

4x2

2x2

2)(x

x

2y

x3

x

7

(2 x

HD : PT(1)
222)

5
y

2

HD : PT(2)

221)

x2y

y

2y

HD : PT(1)

y

2 y)

0

8

2

4y

5y)

5y

(x

x

2y)( x

3x y

2x

2

(0; 0),(1;1)

2) x 2

2x 2

( x

(x

2

HD : PT(1)

0

(y

y

x2

1)

(2)

1

HD : PT(1)

x3

2x x

2 xy

2) y

4

(1)

y y

x(x

2y

( x

217)

0

2 y

HD : PT(1)
Voi : x

x

5)

( 2; 1)

(2)

...