bt phương trình và hệ phương trình hay
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BÀI TẬP PHƯƠNG TRÌNH VÔ TỶ -0985.873.128
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
34.
322323
22
−++−=+++− xxxxxx
35.
xxxxxxxx 32222
2222
+++=+++
36.
)17)(1()6)(1(3)72)(1( +−=−−++− xxxxxx
37.
xxxxxxx 223233
2223
+++=++++
38.
111
32
++=+−++ xxxxxx
39.
111
2422
+++=+−+++ xxxxxxxx
40.
322323
22
−++−=+++− xxxxxx
41.
13
2
2
11
1 =++−+++
x
xx
xx
x
42.
37221223
2
+++=+++ xxxxxx
43.
2352122
3
2
=−+−−+
+
xxxx
x
x
44.
3
8
28
3
24
2
+
+
++=++
+
+
x
x
xxxx
x
x
45.
3 2
3
3 2
3
1 xxxxx ++=++
46.
11
4
23
4
=+−++ xxxx
47.
22
22
2
22
2
=
+−
−
+
++
+
x
x
x
x
48.
xx
x
x
−=−−
−
123
23
2
(Đề 124)
49.
2
2
1
2
1
1
2
33
=++
+ xx
x
(GT-95)
50.
xxxx 4342
32
+=++
51.
22
291 xxx +−=+
52.
11
4
5
1
4
5
2222
+=−−−+−+− xxxxx
53.
21212 =−−−−+ xxxx
(BCVT-00)
54.
2
3
1212
+
=−−+−+
x
xxxx
(TCKT-95)
55.
211
2
4
2
=−++−− 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
+=−+
56.
713
22
=+−−− xxxx
57.
43132
22
+=+−+ xxxx
58.
xxxx −=+++ 91232
22
59.
2242
22
−=+−− xxxx
60.
xxxx 6235352
22
−=+++
61.
1952252
22
=−++++ xxxx
62.
12824484
222
++=+++++ xxxxxx
63.
36333
22
=+−++− xxxx
(TM-98)
64.
123
22
=−+−+−
xxxx
(NT-99)
65.
0221)2(
=+−−−
xxx
(*)
66.
1)1(
4
29
1
2
−−=−+
xxxx
(*)
67.
999
2
++−=−+ xxxx
(*)
68.
)121(11
22
xxx −+=−+
69.
8)6)(2(62 =−++−++ xxxx
70.
41211
2
=−+++−
xxx
71.
4)5)(2(52 =−++−++ xxxx
(CĐBK-06)
72.
5)4)(1(41
=−++−++
xxxx
(NN-01)
73.
22
4324 xxxx −+=−+
(MĐC-01)
74.
11
2
=+−++
xxxx
(ĐHHP-00)
75.
234413
2
−=−−−−+− xxxx
(ĐHHP-01)
76.
2
31
1
=
−
+
− x
x
x
x
(ĐHTL-01)
77.
224222
2
+−−=+−− xxxx
(CĐSP-01)
78.
xxxxx 32312
2
+=−+++
79.
93232
222
=+++++
xxxxx
80.
7109223522
2
−+++=+++ xxxxx
81.
)13)(4(241341 +++=++++ xxxxx
95.
x
xxxxx
4
262
22
+=+++++
96.
52321252
22
+=+++++ xxxxx
97.
11
22
++=++ xxxx
98.
xxxx ++=++
22
11
99.
3 33 3
211 ++=+++ xxxx
100.
xxxxx 3112
22
=+−+++
101.
1)1()1(
3
2
3
3
2
=++++
xxxx
102.
3)4(20)5(
3
23 2
3
2
=−+−−−+ xxxx
103.
119)13()13(
3
2
3
2
3
2
=−+−++
xxx
104.
3318)3()6(
3 2
3
2
3
2
=−−−−++ xxxx
105.
444
121 +=++ xxx
106.
22
)2(2 xx −=−
107.
1000800011000
2
=+−− xxx
108.
3
3
2
1
12
+
+=
x
x
109.
3
3
2332 −=+ xx
110.
3
3
1221 −=+ xx
111.
255336853
23
3
−+−=− xxxx
112.
16
152
588
2
+
=−+
x
xx
113.
28
94
77
2
+
=+
x
xx
82.
253294123
2
+−+−=−+− xxxxx
(QS97)
83.
93232
2
=+++++ xxxxx
84.
1313214
2
+=+−++ xxxxx
85.
)3(43262
2
++=+++ xxxxx
86.
)2(3422
2
xxxx −+=+−
87.
xxxx 51)34(41
2
=−−++
88.
)3(4326
2
++=+−++ xxxxxx
89.
1212
2
=+++++
xxxxx
90.
41292
22
+=+−+++ xxxxx
91.
211
22
=+−+++ xxxx
92.
xxxxx 211
22
++−=++
93.
113 +=−−+ xxx
94.
41292
22
+=+−+++ xxxxx
114.
11
2
=++ xx
(XD-98)
115.
615 =−++ xx
116.
xx 31
2
3
12 ++=
(*)
117.
3
2
1
3
2
1
3
2
1
32 ++++= xx
(*)
118.
534
2
+=−− xxx
119.
513413
2
−+−=+ xxx
120.
3
3
8
7
72
+
+=
x
x
121.
08563232
3
=−−+− xx
(A09)
122.
121522
3
=++− xx
123.
17
3
=−+ xx
(L-96)
124.
112
3
−−=− xx
(TCKT-00)
125.
11217
3 2
4
2
=−−− xx
126.
312
3
=++− xx
127.
)2(3110
23
+=+ xx
128.
)2(3110
46
+=+ xx
129.
15217
23
−+=− xxx
130.
3
1
8
8
2
3
=
+
+
x
x
131.
xxx 231838
32
=++−
132.
243552)2(2
2233
−+=+++−+ xxxxxxx
133.
3332
2
+=++ xxxx
134.
24
873
8
2
+
++
=+
x
xx
x
135.
xxxx 522)1(215
2
−=+++
136.
1212)1(2
22
−−=−+− xxxxx
137.
1221)14(
22
++=+− xxxx
144.
23322210 +=+++ xxx
145.
86738
2
+=++ xxxx
146.
33342
2
−+=+ xxxx
147.
93128333)3(
23
−++=++++ xxxxxx
148.
0642532
2
=−−+−+− xxxx
149.
141232532
2
+−=−+− xxxx
150.
15242
2
−−=−+− xxxx
151.
)121(214
2
3
3
−−+=+− xxxx
152.
11
2
=++++ xxxx
153.
314 =−+++ xxx
154.
xxx −=+− 212
155.
4222
4
42
=−+−+ xxx
156.
2152
2
=−++− xxx
(NN-99)
157.
11414
2
=−+− xx
158.
xx
x
x
−+=
−+
+
1
13
2
138.
2
12
122
+=
++
+++
x
xx
xxx
139.
xxxxxx 2)34)(13(
22
=++++−+
(*)
140.
12234334
2
−++=++ xxxxx
141.
7134 +=−−+ xxx
142.
62213412
22
++=+++− xxxxxx
143.
814426 +=+−+ xxx
159.
2233
2
=−+−++ xxx
160.
1324 −=+−+ xxx
161.
2121)1(
+=+++−
xxxx
162.
42
1
5
1
2
++=++ x
x
x
x
163.
35262 +++=++ xxx
164.
xxxx 33248
4
++=+++
165.
3535
3322423 +++=+++ xxxx
165A.
33
3 23 2
20102009620107320093 =+++−−+− xxxxx
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
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
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.
++=
=
+
+
+
13
2
1
2
)1(
2
2
)1(
2
yxxy
x
y
y
x
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
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
45.
=++
=−−
15))((
3))((
22
22
yxyx
yxyx
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
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
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
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
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
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
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
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
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
