Bài soạn He PT On vao truong chuyen
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BÀI TẬP HỆ PHƯƠNG TRÌNH
Giải các hệ phương trình sau :
1.
+ + = −
−
+ = −
2 2
1
( 99)
6
x xy y
MTCN
x y y x
2.
+ =
−
− + =
2 2
4 2 2 4
5
( 98)
13
x y
NT
x x y y
3.
+ =
−
+ =
2 2
3 3
30
( 93)
35
x y y x
BK
x y
4.
+ =
−
+ = +
3 3
5 5 2 2
1
( 97)
x y
AN
x y x y
5.
+ + =
−
+ + =
2 2
4 4 2 2
7
( 1 2000)
21
x y xy
SP
x y x y
6.
+ + =
−
+ + + =
2 2
11
( 2000)
3( ) 28
x y xy
QG
x y x y
7.
( )
=−−
=++++
6)1)(1(
3)1(1
22
yx
yyxx
8.
( ) ( )
=++++
=++
17)1()1(
811
xyyyxx
yx
9.
−=+−
−=++
)(6
)(7
22
222
yxyxyx
yxyxyx
10.
=−−
=−−+
36)1()1(
12
22
yyxx
yxyx
11.
=+++
=+
4
11
2
yx
yx
x
y
y
x
15.
=−+
=++
2222
2222
3
yxxyyx
yxxyyx
16.
+ + =
−
+ + =
2
( 2)(2 ) 9
( 2001)
4 6
x x x y
AN
x x y
17.
+ + =
−
+ + − =
2
(3 2 )( 1) 12
( 97)
2 4 8 0
x x y x
BCVT
x y x
18.
+ =
−
+ + =
2 2 3 3
4
( 2001)
( )( ) 280
x y
HVQHQT
x y x y
19.
+ + =
−
+ + =
2 2
2 2
1
( )(1 ) 5
( 99)
1
( )(1 ) 49
x y
xy
NT
x y
x y
20.
( )
=
++
+=+
24
1
1
)1(2)1(
22
22
22
yx
yx
yxxy
21.
+ + + =
−
+ + + =
2 2
2 2
1 1
4
( 99)
1 1
4
x y
x y
AN
x y
x y
22.
=++
=
+
+
+
6)
1
1)((
3
2
11
22
xy
yx
y
y
x
x
23.
=+++
=+++
4
1
622
22
y
x
x
y
xy
xy
xyxyxyyx
12.
=+++
=+++
4
4
22
x
y
y
x
yx
x
y
y
x
yx
13.
=−+
=++
1
11
3
22
xy
yx
xyyxyx
14.
++=
=
+
+
+
13
2
1
2
)1(
2
2
)1(
2
yxxy
x
y
y
x
24.
=
++
=+
5
1
1)(
4
1
xy
yx
xy
xy
25.
=
++
=
++
18
1
1)(
6
1
1)(
2
22
xy
yx
xy
yx
26.
=
++
=
++
27
1
1)(
9
1
1)(
3
33
2
22
xy
yx
xy
yx
27.
−=−
−=−
232
232
22
22
xyy
yxx
(QG-00)
28.
−=
−=
xyy
yxx
3
3
2
2
(MTCN-98)
29.
+=
+=
xyy
yxx
23
23
2
2
30.
+=
+=
x
x
y
y
y
x
1
2
1
2
2
2
31.
= +
−
= +
3
3
3 8
( 98)
3 8
x x y
QG
y y x
39.
−
=
−
=
2
2
1
2
1
2
x
x
y
y
y
x
40.
−=+
−=+
22
22
22
22
xyxy
yxyx
41.
=−−
−=++
732
13
22
22
yxyx
yxyx
42.
=+
=+
5
10
23
23
xyy
xyx
43.
=+−
−=+−
133
13
22
22
yxyx
yxyx
44.
=−
=−
19
2)(
33
2
yx
yyx
55.
+=+
=++
yxyx
yxyx
3
1
33
22
56.
++=+
−=−
2
3
yxyx
yxyx
57.
=+
−=−
4
263
22
2
yx
xyxyy
58.
=++
=++
3
42
2
2
xxyx
yxyx
59.
=++
=++
75
522
2
2
xxyy
yxyx
60.
=++−
=++
945
3
2
22
yxxyy
xyyx
2
32.
+=
+=
xyy
yxx
2
2
3
3
33.
+=
+=
xyy
yxx
5
5
3
3
34.
−=
−=
12
12
3
3
xy
yx
35.
+=
+=
223
223
23
23
xyy
yxx
36.
+ =
−
+ =
1 3
2
( 99)
1 3
2
x
y x
QG
y
x y
37.
=+
=+
2
2
3
2
3
2
y
xy
x
yx
(TL-01)
38.
+
=
+
=
2
2
2
2
2
3
2
3
y
x
x
x
y
y
45.
=++
=−−
15))((
3))((
22
22
yxyx
yxyx
46.
=++
=−−
175))((
7))((
22
22
yxyx
yxyx
47.
=++
=++
422
42
22
22
yxyx
yxyx
48.
=−
=+
xyx
xyx
33
33
2
2
49.
=+
=+
xyxy
yxyx
32
2
2233
50.
=+−
=++
122
222
222
222
xyyxyx
xxyx
51.
=++
=+
222
22
31
2)1(
xxyyx
yx
52.
=+
=+
3333
3
32
2
yxyx
xyyx
53.
+=
=−+
yxx
xyyx
3
22
2
1
54.
+=+
=++
xyyx
yxyx
22
3
33
22
61.
−+=+
=++
9572
3
2
22
yxxyx
xyyx
62.
=−−++
=+
22
2
22
22
xyyxxyyx
yx
63.
=+
=+
32
32
2
2
yxx
xyx
64.
=+
=+−
2
44)1(
22
2
yx
yyx
65.
+=
−=−
12
11
3
xy
y
y
x
x
(A-03)
66.
−=+++
−=++++
4
5
)21(
4
5
24
232
xxyyx
xyxyyxyx
(A-08)
67.
+=+
+=++
662
922
2
2234
xxyx
xyxyxx
(B-08)
68.
−=−−
−=++
xxxyyx
yxyxxy
2212
2
22
69.
=+−+−−
−+=
01681645
)4)(45(
22
2
yxxyxy
xxy
70.
=−++
=+++
yxyx
yxyyx
)2)(1(
4)(1
2
2
71.
=
+
+
=
+
+++
3
)(
1
2
7
)(
3
)(44
2
22
yx
x
yx
yxxy
72.
=−−+
=−−
3342
1623
22
yxyx
yxxy
73.
=−
=+
6)2(
8)32(
3
3
yx
yx
74.
=+
=+−
1
32
22
22
yx
xyx
75.
=+
=+
162
2
1
23
22
xyx
yx
76.
=+
=+
13
3
22
23
yx
yxyx
77.
=
+
++
=
++
4
1
4
1
1)(
22
xy
yx
xy
xy
xy
yx
78.
=
++
=++−+
8
1
1)(
02)62(
2
22
xy
yx
xyyxxy
81.
=+++
=+++
4
11
4
22
22
y
x
x
y
yx
xyyxyx
82.
=+
+=+
13
)1()1(
22
22
yx
yxxy
83.
−−=
++−=
262
43
3
3
yyx
xxy
84.
+=
+−
+
+=
+−
+
xy
yy
xy
y
yx
xx
xy
x
2
3
2
2
3
2
92
2
92
2
85.
++=+
++=+
321
321
xy
yx
(*)
86.
=+++
=+++
11
24
yyy
yxx
87.
=++
=++
11
24
4
4
yx
yx
88.
=+−+++
=−
524352
32
yxyx
yx
89.
=++
=+
17
7
22
xyyx
yx
90.
−+=+−
=++
33223
35
yxyx
yx
92.
=−−+−−
=+
3354
43
yxyx
x
y
y
x
93.
=−++
=−++
8
4
2222
yxyx
yxyx
94.
=+
=++
4
282
22
yx
xyyx
95.
=+
+=+
6
)(3)(2
3
3
3
2
3
2
yx
xyyxyx
96.
+ = +
−
+ =
7
1
( 99)
78
x y
y x
xy
HH
x xy y xy
97.
=
=+
9
3
411
xy
yx
98.
=−+
=−+
22
22
xy
yx
99.
=++
=++
224
224
xy
yx
100.
=++
=++
11
11
xy
yx
101.
=−++
=−++
479
479
xy
yx
4
79.
=++
=++
3
1
4
1
2
2
x
xyx
x
yx
80.
=++
=++
3
11
42
2
2
y
x
xy
x
xyxyyx
91.
−=+−
+=+
222
1
2
yyx
xyx
102.
+ + − =
−
+ + − =
5 2 7
( 1 2000)
5 2 7
x y
NN
y x
103.
=+++
=++++
71312
722
yx
yxyx
104.
=+++
−+−+−=+++++
80
531531
22
yxyx
yyyxxx
105.
=+++++++
=+++
61111
311
yxxyyx
yx
106.
+ + + + + + + + + =
−
+ + + − + + + + − =
2 2
2 2
1 1 18
( 99)
1 1 2
x x y x y x y y
AN
x x y x y x y y
107. Giả sử hệ
=++
=++
1
2
222
zxyzxy
zyx
có nghiệm (x, y, z): CMR :
3
4
,,
3
4
≤≤−
zyx
