BÀI TẬP GIẢI HỆ PHƯƠNG TRÌNH ĐỐI XỨNG (PHẦN 1)
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Bài 1 Giải các hệ phương trình sau trên tập hợp số thực
4, 1,
2
2,
2,
164
3,
8, 4,
5
2, 5,
1
208, 6,
96
55, 7,
24
7, 8,
3
2
9,
xy
xy
x
+ + =
− =
+ + =
+ = −
=
=
2
1, 0
2, 10,
1
1, 11,
1
1, 12,
3
13,
14,
6
15,
1
16,
x y xy
+ − = −
= + −
+ =
+ +
3, 2
y
x y y x
=
4, 17,
4, 1,
18,
7, 5, 19,
35, 2, 20,
2, 4, 21,
2, 7, 22,
2
23,
160
24,
2
xy x y
xy x y
x y y x
+ =
+ =
+ =
5, 25,
2
11, 26,
1
4, 27,
2
2 3 2, 28,
14
7, 29,
21
5, 30,
13
5, 31,
13
xy x y
32,
8
Trang 2
( )( )
30, 1,
35
2, 2,
2
7, 3,
2
11,
11
18, 5,
6,
5, 7,
x y xy
xy x y
xy x y
xy
+ + =
+ + + =
9
2, 8,
2
10, 9,
73
1, 10,
1
1
13, 11,
1
12
1
12,
1
4
13,
1
1
xy
xy
xy
xy
+
4,
2
2
3
2
2 ,
15,
1
15, 16,
85
1
17,
1
1
18,
1
19,
xy
xy
xy
xy
xy
+
( )
2
2 2
4
1 1
20,
1
21,
1 4
10 , 3 22,
5
20,
4
x x
xy
xy xy
x y y x
xy
+ =
Trang 3
2 2
3, 1,
2,
3,
1, 4,
2
7, 5,
13
1
2, 7,
4
8,
xy
+ =
+ + + =
2 2
2
1 , 2
9,
3, 10,
6
1
13, 11,
1
12
12, 12,
13
7, 13,
xy
xy
x y xy
x y xy
+ + =
175
14,
y
=
= −
3, 15,
17
18, 16,
17,
4
18,
3 , 19,
15
2, 20,
1
2, 21,
xy x y
− =
+ =
+
=
−
2
6
1, 22,
1
1, 23,
1
12, 24,
1 3 82, 25,
3
2, 26,
1
27,
28,
29,
xy
xy
xy
− + =
+ =
=
=
+ =
+
=
2,
+ + + =
Trang 4
2
5, 1,
4, 2,
5, 3,
22
4, 4,
78, 5,
97
481, 6,
37
1 7,
x
y
+ + =
+ + =
+ =
+ + + =
2
2 2
2 2
2 2
7, 5
2, 8,
3
9,
3,
10,
11,
3
13,
x
y x
x
y
x
y
+ + =
+ + =
=
3, 14,
3
5, 15,
2, 16,
4, 17,
4
2, 18,
19,
20,
x
+ + + =
2 2
2 2
2
2 2
2,
2
21,
22,
1, 3
23,
24,
25,
1 26,
y y
x
y
y
+
− =
+ + =
+
+ + =
+ =
+ = + 5 ,
1
x
y x
x
+ + =
−
Trang 5
( )( )
2
2
2
1,
2,
1,
3,
4,
2
5,
4
6,
x
x
− − + =
2
2
2
2
7,
8,
9,
10,
11,
2 12,
( )
2
2 , 8
13,
14,
15,
y
x
+ + =
( ) ( )
2
2
2
17,
18,
19,
20,
21,
22,
( )
2 2
2
2 2
2
23,
1 3
24,
25,
26,
1 27,
+ = +
( ) ( )
( ) ( )
2
2
2
2 2 2
2 2
28,
29,
30,
31,
32,
y
Trang 6( )
( )
2 2
2
2
2
2
2
2 2
1,
2,
3,
4,
5,
1 2 ,
6,
x y
= +
+ =
2
2
2
2
2
2
2
7,
8,
9,
10,
11,
12,
+
2
2
2
2
2
2 2
7,
13,
14,
15,
16,
y
( )
2
2
2
2
17,
18,
19,
20,
1
3, 21,
( ) ( )
2
2 2
2 2
2 2 2
2
1 2
22,
23,
24,
2 2
4, 2
26,
3
2
27,
xy
y
x
x
y
y
−
=
+ = +
+
−
2
2
2
5,
28,
2
2 29,
1
y
x
y
+ −
+ + =
−
−
=