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BÀI TẬP PHƯƠNG TRÌNH VÔ TỶ
1.
126
22
=−+ xx
(VH-98)
2.
3111
22
=++ xx
3.
2381716 −=+ xx
(QG-D-97)
4.
xxx −=−− 1251
2
(TCKT-97)
5.
02193
2
=−++− xxx
6.
)4(382
2
−=−− xxx
(BD-01)
7.
94)3(
22
−=−− xxx
(Y HCM-01)
8.
1266
2
−=+− xxx
(XD-01)
9.
14
2
=++ xxx
(HVCTQG HCM-00)
10.
1223
2
−=+− xxx
11.
231034 −=−− xx
(HSGQG-01)
12.
1313 −=++ xx
13.
4235 +=++− xxx
(HH-98)
14.
31243 +=−−+ xxx
(NH-98)
15.
36333
22
=+−++− xxxx
(TM-98)
16.
53322 −=−−+ xxx
(BK-94)
17.
42533 −=−−− xxx
(A05)
18.
3200820098
22
++−=+ xxx
19.
411222 =+−+++ xxx
(D05)
20.
811 +−=−+ xxx
21.
333
3221 −=−+− xxx
(Đề 113)
22.
1334
33
=−−+ xx
(Đề 12)
23.
333
511 xxx =−++
24.
333
121216 −=+− xxx
25.
2
2)2()1( xxxxx =++−
(SP2-A00)
26.
x
x
xx
x
11
1
1 −
=−−−
27.
221682
22
+=−+++ xxxx
28.
0)1(12
2
=−+−−−− xxxxxx
29.
62)22(3 ++=−+ xxx
(KTQS-01)
30.
342123
2
+++=+++ xxxxxx
31.
1
1
2
21 =
+
+
++−+
x
x
xx
32.
(
)
(
)
1111
22
=−+++ xxxx
33.
xxxx 33)2)(5(
2
+=−+
34.
126
22
=++ xx
(VH-98)
35.
322323
22
−++−=+++− xxxxxx
36.
xxxxxxxx 32222
2222
+++=+++
37.
)17)(1()6)(1(3)72)(1( +−=−−++− xxxxxx
38.
xxxxxxx 223233
2223
+++=++++
39.
111
32
++=+−++ xxxxxx
40.
111
2422
+++=+−+++ xxxxxxxx
41.
322323
22
−++−=+++− xxxxxx
42.
3
2
12
11
1 +++=+++
x
xx
xx
x
43.
37221223
2
+++=+++ xxxxxx
44.
3522122
3
2
−++=−+
+
xxxx
x
x
45.
3
8
28
3
24
2
+
+
++=++
+
+
x
x
xxxx
x
x
46.
3
2
3
3
2
3
1 xxxxx ++=++
47.
4
23
4
11 xxxx ++=++
48.
22
22
2
22
2
=
+−
−
+
++
+
x
x
x
x
49.
xx
x
x
−=−−
−
123
23
2
(Đề 124)
50.
2
2
1
2
1
1
2
33
=++
+ xx
x
(GT-95)
51.
xxxx 4342
32
+=++
52.
22
291 xxx +−=+
53.
11
4
5
1
4
5
2222
+=−−−+−+− xxxxx
54.
21212 =−−−−+ xxxx
(BCVT-00)
55.
2
3
1212
+
=−−+−+
x
xxxx
(TCKT-95)
56.
211
2
4
2
=−++−− xxxx
57.
713
22
=+−−− xxxx
58.
43132
22
+=+−+ xxxx
59.
xxxx −=+++ 91232
22
60.
2242
22
−=+−− xxxx
61.
xxxx 6235352
22
−=+++
Tài liệu bồi dưỡng Đại số 10
1
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62.
12824484
222
++=+++++ xxxxxx
63.
1952252
22
=−++++ xxxx
64.
36333
22
=+−++− xxxx
(TM-98)
65.
123
22
=−+−+− xxxx
(NT-99)
66.
0221)2( =+−−− xxx
(*)
67.
1)1(
4
29
1
2
−−=−+ xxxx
(*)
68.
999
2
++−=−+ xxxx
(*)
69.
)121(11
22
xxx −+=−+
70.
8)6)(2(62 =−++−++ xxxx
71.
41211
2
=−+++− xxx
72.
4)5)(2(52 =−++−++ xxxx
(CĐBK-06)
73.
5)4)(1(41 =−++−++ xxxx
(NN-01)
74.
22
4324 xxxx −+=−+
(MĐC-01)
75.
11
2
=+−++ xxxx
(ĐHHP-00)
76.
234413
2
−=−−−−+− xxxx
(ĐHHP-01)
77.
2
31
1
=
−
+
− x
x
x
x
(ĐHTL-01)
78.
224222
2
+−−=+−− xxxx
(CĐSP-01)
79.
xxxxx 32312
2
+=−+++
80.
93232
222
=+++++ xxxxx
81.
7109223522
2
−+++=+++ xxxxx
82.
1)13)(4(24134 −+++=+++ xxxxx
83.
253294123
2
+−+−=−+− xxxxx
(QS97)
84.
93232
2
=+++++ xxxxx
85.
1313214
2
+=+−++ xxxxx
86.
)3(43262
2
++=+++ xxxxx
87.
)2(3422
2
xxxx −+=+−
88.
xxxx 51)34(41
2
=−−++
89.
)3(4326
2
++=+−++ xxxxxx
90.
1212
2
=+++++ xxxxx
91.
41292
22
+=+−+++ xxxxx
92.
211
22
=+−+++ xxxx
93.
xxxxx 211
22
++−=++
94.
113 +=−−+ xxx
95.
x
xxxxx
4
262
22
+=+++++
96.
41292
22
+=+−+++ xxxxx
97.
52321252
22
+=+++++ xxxxx
98.
11
22
++=++ xxxx
99.
xxxx ++=++
22
11
100.
3
3
3
3
211 ++=+++ xxxx
101.
xxxxx 3112
22
=+−+++
102.
1)1()1(
3
2
3
3
2
=++++ xxxx
103.
3)4(20)5(
3
2
3
2
3
2
=−+−−−+ xxxx
104.
119)13()13(
3
2
3
2
3
2
=−+−++ xxx
105.
3318)3()6(
3
2
3
2
3
2
=−−−−++ xxxx
106.
444
121 +=++ xxx
107.
22
)2(2 xx −=−
108.
1000800011000
2
=+−− xxx
109.
3
3
2
1
12
+
+=
x
x
110.
3
3
2332 −=+ xx
111.
3
3
1221 −=+ xx
112.
255336853
23
3
−+−=− xxxx
113.
16
152
588
2
+
=−+
x
xx
114.
28
94
77
2
+
=+
x
xx
115.
11
2
=++ xx
(XD-98)
116.
615 =−++ xx
117.
xx 31
2
3
12 ++=
(*)
118.
3
2
1
3
2
1
3
2
1
32 ++++= xx
(*)
119.
3
3
8
7
72
+
+=
x
x
120.
534
2
+=−− xxx
121.
513413
2
−+−=+ xxx
122.
08563232
3
=−−+− xx
(A09)
123.
121522
3
=++− xx
124.
17
3
=−+ xx
(L-96)
125.
112
3
−−=− xx
(TCKT-00) 138.
141232532
2
+−=−+− xxxx
Tài liệu bồi dưỡng Đại số 10
2
Chuyên đề Hệ phương trình ThÇy gi¸o:Phïng §øc TiÖp – S§T: 0985.873.128
126.
11217
3
2
4
2
=−−− xx
127.
312
3
=++− xx
128.
)2(3110
23
+=+ xx
129.
)2(3110
46
+=+ xx
130.
15217
23
−+=− xxx
131.
3
1
8
8
2
3
=
+
+
x
x
132.
3332
2
+=++ xxxx
133.
24
873
8
2
+
++
=+
x
xx
x
134.
xxxx 522)1(215
2
−=+++
135.
1212)1(2
22
−−=−+− xxxxx
136.
1221)14(
22
++=+− xxxx
137.
0642532
2
=−−+−+− xxxx
139.
15242
2
−−=−+− xxxx
140.
)121(214
2
3
3
−−+=+− xxxx
141.
11
2
=++++ xxxx
142.
314 =−+++ xxx
143.
2152
2
=−++− xxx
(NN-99)
144.
11414
2
=−+− xx
145.
xx
x
x
−+=
−+
+
1
13
2
146.
2233
2
=−+−++ xxx
147.
1324 −=+−+ xxx
148.
2121)1( +=+++− xxxx
149.
42
1
5
1
2
++=++ x
x
x
x
150.
35262 +++=++ xxx
151.
xxxx 33248
4
++=+++
152.
3535
3322423 +++=+++ xxxx
154.
xxxxxx 2)34)(13(
22
=++++−+
155.
33
3
2
3
2
20102009620107320093 =+++−−+− xxxxx
Tài liệu bồi dưỡng Đại số 10
3
Chuyên đề Hệ phương trình ThÇy gi¸o:Phïng §øc TiÖp – S§T: 0985.873.128
BÀI TẬP HỆ PHƯƠNG TRÌNH
Bài 1 : 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
12.
=+++
=+++
4
4
22
x
y
y
x
yx
x
y
y
x
yx
13.
=−+
=++
1
11
3
22
xy
yx
xyyxyx
14.
=−+
=++
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
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
Tài liệu bồi dưỡng Đại số 10
4
Chuyên đề Hệ phương trình ThÇy gi¸o:Phïng §øc TiÖp – S§T: 0985.873.128
15.
++=
=
+
+
+
13
2
1
)1()1(
2
2
2
2
yxxy
x
y
y
x
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
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
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
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
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
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
Tài liệu bồi dưỡng Đại số 10
5
Chuyên đề Hệ phương trình ThÇy gi¸o:Phïng §øc TiÖp – S§T: 0985.873.128
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
79.
=++
=++
3
1
4
1
2
2
x
xyx
x
yx
80.
=++
=++
3
11
42
2
2
y
x
xy
x
xyxyyx
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
91.
−=+−
+=+
222
1
2
yyx
xyx
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
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
Tài liệu bồi dưỡng Đại số 10
6