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2. Tiết 1.Dạng 2: Giải phương trình
3. Tiết 1. Dạng 3: Giải bất phương trình
4. Tiết 1. Dạng 4: Giải hệ bất phương trình
5. Tiết 1. Dạng 5: Phương trình, bất phương trình chứa tham số
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yxf
là hệ đối xứng loại I nếu



=
=
L\OL\O
L\OL\O
xygyxg
xyfyxf
2)Cách giải : - Đặt
x y S
xy P
+ =


=

. ĐK:

S P
.
- Biểu thị hệ qua S và P .
- Tìm S ; P thoả mãn điều kiện
PS


.
Khi đó x; y là 2 nghiệm của phơng trình :

=
=
L\O
L\O
yxg
yxf
là hệ đối xứng loại II nếu :
L\OL\O yxgxyf =
2)Cách giải :
A&)&B^H6

+)Đối với hầu hết các hệ dạng này khi trừ 2 vế ta đều thu đợc phơng tình :
(x-y).h(x;y) = 0
Khi đó hệ đã cho
O \ L
O \ L O \ L
x y h x y
f x y f x y
= =
= =

( Chú ý : Có những hệ đối xứng loại II sau khi trừ 2 vế cha xuất hiện ngay x - y = 0 mà phải suy luận
tiếp mới có điều này).
+) Phơng pháp điều kiện cần và đủ:
Phơng pháp này đ ợc áp dụng tốt cho hệ đối xứng với yêu cầu: Tìm giá trị tham số để hệ có nghiệm
duy nhất.
Đ/k cần:

B ớc 1 : Rút y theo x ở phơng trình bậc nhất (1) rồi thế vào phơng trình bậc hai (2) , ta đợc phơng
trình bậc hai ẩn x có dạng : A
1
x
2
+ B
1
x + C
1
= 0 (*) .
B ớc 2 : Giải pt (*) tìm đợc x thế vào (1) ta tìm đợc y .
3/ Chú ý :
3.1.Số nghiệm của hệ ( I ) phụ thuộc vào số nghiệm của pt (*) .
Nếu pt (*) vô nghiệm thì hệ đã cho vô nghiệm .
Nếu pt (*) có nghiệm duy nhất x
0
thì hệ đã cho có nghiệm duy nhất (x
0
; y
0
) .
Nếu pt (*) có 2 nghiệm phân biệt x
1
; x
2
thì hệ đã cho có 2 nghiệm phân biệt (x
1
; y
1
) và




3/

PSY OL
jP h S PShY OL



4/

PSY OL
SPY OL



d) Giải các hệ phơng trình sau :


PSYj
P S Yj





PSPSY
P SP Y


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