Bài9:Ghpt
x y
3x 2y 6 3x 2y 6
1
a)
2 3
2x y 11 4x 2y 22
2x y 11
28
7x 28 x 4
x 4
7
2x y 11 y 3
y 11 2x
(x 1)(y 2) xy 8 xy 2x y 2 xy 8
b)
(x 1)(y 3) xy 1 xy 3x y 3 xy 1
2x y 6 5x
3x y 4
− = − =
− =
⇔ ⇔
+ = + =
+ =
= =
= =
⇔ ⇔ ⇔
+ = =
= −
+ + = + + + + = +
⇔
− + = + + − − = +
+ = =
⇔ ⇔
− =
10 x 2
3x y 4 y 2
=
⇔
− = =
o
2
1 2
o
2
o
1 2
o
Bài10(21) Ghpt
x y 5
Theo viet x, y là n pt :
xy 4
t 5t 4 0
a b c 0 t 1; t 4
Hpt có n : (x 1, y 4);(x 4, y 1)
x y 1 x ( y) 1
b)
xy 6 x( y) 6
Theo viet x, y là n pt : t t 6 0
t 2; t 3
Hpt có n : (x 2, y 3);(x 3, y 2)
+ =
=
− + =
⇔ + + = ⇔ = =
= = = =
− = + − =
⇔
= − = −
− − − =
⇔ = − =
= − = − = =
a)
+ + =
+ =
+ = = ⇔ + + =
⇔ + = −
+ = + =
+ − =
⇔ ⇔ ⇔
− = − = + =
=
=
=
⇔ ⇔
−
= −
= −
=
2 2
2 2 2
2 2 2
2
2 2
B i11(21)à
x y xy 5
(1)
x y 5
§ Æt x y a;xy b x y 2xy a
x y a 2b
a b 5 2a 2b 10
a 2a 15 0
Pt (1)
a 2b 5 a 2b 5 a b 5
a 3
3
b 2
a
5
a 5
b 5 a
b 10
− =
− + = − =
⇔ ⇔
− = −
+ = + =
+ =
− = − = =
+ = + = + =
⇔ ⇔ ⇔
− = − − = − = −
+ = + = + =
=
=
⇔
2 2 2
Bµi12 :Ghpt
2x y 3
4x 4xy y 9 (2x y) 9
2x y 3
x 3y 5 x 3y 5
x 3y 5
2x y 3 6x 3y 9 7x 14
x 3y 5 x 3y 5 x 3y 5
2x y 3 6x 3y 9 7x 4
x 3y 5 x 3y 5 x 3y 5
x 2
y
−
=
=
1
4
x
7
13
y
7
− + = − − + + − =
⇔
+ = + =
− − − + − =
⇔
+ =
− − − + − = − − + =
⇔ ⇔
+ = + =
− =
+ =
⇔
− + =
+ =
2 2
2 2 2 2
2
2 2
2 2 2 2
2 2
2 2
Bµi13 : Ghpt
6x 3xy x 1 y 6x 3xy x y 1 0
1)
x y 1 x y 1
(6x 2x) (3xy y) (3x 1) 0
x y 1
2x(3x 1) y(3x 1) (3x 1) 0 (3x 1)(2x y 1) 0
x y 1 x y 1
3x 1 0
x y 1
2x y 1 0
x y 1
=
=
=
+ =
⇔ ⇔
= +
= +
+ =
+ + =
=
= ± = ±
=
⇔
=
= + = +
−
⇔ ⇔
=
+ + = + =
−
=
2
2 2
2 2
2 2
2 2 2
1
1
x
x
3
3
8
y
x y 1
9
y 2x 1
y 2x 1
x y 1
x (2x 1) 1
1
x
3
8 2 2
y
9 3
x 0
y 1
y 2x 1 y 2x 1
4
x
x (2x 1) 1 5x 4x 0
5
3
y
5
+ + − = + = −
⇔
+ − + = − + − =
< ⇔ = ⇔ =
≥ ⇔ = ⇔ =
+ = = =
⇔ + = ⇔ ⇔
+ = − = − =
Bµi14.Ghpt
x 1 y 1 5 x 1 4y 4
x 1 4y 4 0 4y 4 y 1 5(1)
8
Víi y 1, (1) 3y 8 y (lo¹i)
3
Víi y 1, (1) 5y 10 y 2
x 1 4 x 3, y 2
x 1 4
x 1 4 x 5, y 2
2
2
2 2
2
0
Bài15 :Ghpt
2x 2x xy y 0 (1)
x 3xy 4 0 (2)
(1) 2x(x 1) y(x 1) 0
(2x y)(x 1) 0
x 1 0 x 1
2x y 0 y 2x
5
*x 1thay vào (2) 1 3y 4 0 y
3
*y 2x thay vào (2) x 6x 4 0
7x 4(Vô lý) ptvn
5
Pt có n là : x 1; y
3
− + − =
− + =
⇔ − + − =
⇔ + − =
− = =
⇔ ⇔
+ = = −
= ⇔ − + = ⇔ =
= − ⇔ + + =
⇔ = − ⇔
= =
2 2
2 2
2 2 2 2
2 2
2
2
Bài16 :Ghpt
2x 3xy y 3x 1(1)
2y 3xy x 3y 1(2)
(1) (2) 2x 2y y x 3x 3y
3x 3y 3x 3y 0
3(x y)(x y) 3(x y) 0
3(x y)(x y 1) 0
*x y 0 x y ta có (1) 2y 3y 1 0
3 17
y
4
*x y 1 ta có (1) 4y 4y 0 y 0; y 1
− = − −
− = − −
− ⇔ − = − − +
⇔ − + − =
⇔ − + + − =
⇔ − + + =
− = ⇔ = ⇔ − − =
±
⇔ =
= − − ⇔ + = ⇔ = = −
+
0
y 0 x 1
y 1 x 0
3 17 3 17 3 17 3 17
Hpt có n là : (x, y) , ; , ;( 1,0);(0, 1)
4 4 4 4
= ⇔ = −
+ = − ⇔ =
+ + − −
= − −
÷ ÷
÷ ÷