E2 f8 bộ binh

CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 2 – SƯ ĐOÀN 8 – QUÂN ĐOÀN BỘ BINH
1
CHUYÊN ĐỀ PHƯƠNG TRÌNH VÀ BẤT PHƯƠNG TRÌNH
BÀI TẬP SỬ DỤNG ẨN PHỤ (PHẦN 2)
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Bài 1. Giải các phương trình và bất phương trình sau trên tập hợp số thực
( )
( )
( )
( )( )
( )
( )
( )
2 3
3 2
3 2
2 4 2
33 2
2 3
2 3 2
3
33 2
2 3
3 2
2
1, 2 4 5 1
2, 1 1 3
3, 10 8 3 6
4, 3 9 3 3 1 0
5, 3 2 2 6 0
6, 2 5 1 7 1
6
7, 3 2 2 3 4 2
30
8, 2 1 2 3 8
9, 3 3 2 1 0
10, 3 2 10 1
5
11, 2 3
2
12, 2 2 3
x x
x x x
x x x
x x x x
x x x x
x x x
x x x x x
x x x
x x x x
x x
x x x
x x
+ = +
+ − = +
+ = − +
− + + + + =
− + + − =
+ − > −
− − = + + +
− − = +
− − + + =
+ = +
+ + ≤ +
+ +
( )
( )
( ) ( )
( )
( )
( )( )
( )
3 2
2
2
2
2 2 3 23 3
33 2 2
2 3
2 4
2
2 2
3 2
5 5 3 2
13, 2 3 2 3 2
14, 1 2 1
15, 4 12 1 27 1
16, 1 5 1 6 1
17, 1 2 2
18, 1 3 2 4
19, 7 10 14 5 4
20, 11 42 2 11 42
21, 1 2 5 2 1 6
22, 7 1 6 2
23, 2
x x x
x x x x
x x x x
x x x x
x x x
x x x x
x x x
x x x
x x x x
x x x x x
x x
< + + +
− + = −
− + − =
+ + = +
+ + − = −
+ − = −
+ + = +
− + = +
+ + = +
+ − + + = +
+ = +
2
6 23 3
3 2
2
008 4 3 2007 4 3
24, 2 1 1 1
25, 3 1 2 3 1
26, 2012 5 4 2011 5 4
x x x x
x x x
x x x
x x x x
− + = −
+ − − = −
− ≤ + +
− + = −
( )( )
( )
( ) ( )
2
2 4
4 2 2
2 4
2 3
2 3
3 2
2
2 2 3 23 3
2
27, 4 1 5 1
28, 3 1 3 1 8 1
29, 14 10 7 5 1 4
30, 11 1 7 4 6
31, 12 12 12 1
32, 4 6 2 9 1
33, 5 7 3 7 1
34, 1 1 3 5
35, 7 3 1 2 2
36, 1 3 1 4 1
37, 5 4 4 4 6
x x x x
x x x x x
x x x
x x x x
x x
x x x
x x x
x x x
x x x x
x x x
x x x
+ + − =
− + − + =
− + = +
+ + = + +
+ > +
+ + < −
+ + = −
+ − ≤ −
+ − − = +
+ + − = −
− + − + = ( )
( ) ( )
( )( )
( )
( )
22 4
2
4 2 2
2 3
2 4
2
2
2
2
2 4
38, 1 2 1 3 1 1
39, 3 4 4 7 1
40, 5 3 3 8 1 1
42, 4 23 14 16 8
43, 16 8 22 19 4
44, 2 3 1 1 2 25 9
45, 1 3 2 5 8
46, 3 15 2 7 24
1 1
47, 2 2 18 7
2 4
x x
x x x x
x x x x
x x x x x
x x x
x x x
x x x x
x x x x
x x x x
x
x x x
− −
− + − = − +
+ − = −
+ − = − +
+ − = −
+ + = +
+ + + = + +
+ − > + − +
− + − ≤ − +
 +
− + ≤ + −  
 
( )( )
( )
4
3 2
2
2
2
2
48, 2 3 2 2 3 3 2 2
49, 3 1 2 3 1
50, 2 1 3 2 3 2
51, 5 1 2 40 34 10
53, 2 7 2 16 17
54, 5 51 125 5
x x x x
x x x
x x x x
x x x x
x x x x x
x x x x
− + + ≥ − +
− ≤ + +
+ − ≤ − +
+ = + − +
+ − > + − +
− + + = +

2
( )
( )( )
( )
( )
( )
( )
( )
( )
2
2 2
2
222
2
2
2
3 3
2 2
3 2
2
2
2 2
2 2
1, 2 1 19 2 8
2, 3 1 4 3 2
3, 15 2 1 2 5 2
11
4, 1
2 2 1
5, 3 7 8 4 2 8
6, 4 1 1 2 2 1
7, 1 2 2
2 3 1
8, 1
2
3
9, 3 1 2 1 5 3
2
10, 4 7 5 2 1
x x x x
x x x x x x
x x x x
xx
x
x x x
x x x x
x x x x
x x x x
x x x
x x
x
x x x x
x x x x x
+ = + − −
+ − + + + + =
+ + + + =
++
+ + =
−
+ + = + +
− + ≤ + +
− ≤ +
+ − +
− + =
+
+ − = + −
− + + − =
( )
( )
( )
( )
2 2
2 2
2 2 4 2
2 2
2 2
2 2
2
2 2
4 3 2 3
11, 3 2 3 6 2 6 5
12, 3 5 2 3 4 6 1
13, 3 1 1
14, 2 2 1 3 4 1
15, 5 14 9 20 5 1
16, 6 3 1 3 6 19
17, 1 3 2 3 2 2
18, 3 6 2 1 3 1
1
19, 2 2 2 1
x x x x x
x x x x
x x x x
x x x x x
x x x x x
x x x x x
x x x x
x x x x
x x x x x x
+ + + + = +
− − = − +
+ − = − +
+ + − = + +
+ + − − − = +
+ − + − = − +
− + − = − + −
+ + + − = +
+ + − + = +
( )
( )
( )
( )
( ) ( )
2
2 2 2
2 2
2
2 2
2 2
2
2
2 2
20, 3 2 1 2 2
21, 1 2 3 1
22, 2 2 4 4 2 9 16
23, 4 1 1 2 2 1
24, 2 1 2 1 2 1
25, 12 1 36
26, 2 2 2 1
27, 3 2 1 1 1 3 8 2 1
x
x
x x x x
x x x x
x x x
x x x x
x x x x x
x x x
x x x
x x x x
−
+ − + = + +
+ − + = +
+ + − = +
− + = + +
− + − + = +
+ + + =
− = −
+ − = + + +

3
( )
( )
( )
( )
( )
2 2
2
2 2
2 2
2 2
3 2 5 4
2
3 2 3
2
2
2
1, 6 10 5 4 1 6 6 5
2, 1 3 2 1
3, 4 7 4 7
4, 6 3 2 5 3
5, 10 3 1 1 6 3
6, 2 3 1 1
2 37
7, 4 1 9 26 0
3 3
8, 6 2 3 5 1 3
9, 2 6 1 4 5
10, 8 8 1 5
11, 2 4
x x x x x
x x x x
x x x x
x x x x x
x x x x
x x x x x
x x x
x x x x x
x x x
x x x
x
− + = − − +
+ + − = +
+ + = + +
− − + = + −
+ + = + +
− − + = + +
+ − + + =
+ − + = − +
− − = +
+ + = +
+
( )
( )
2
2
2
2
2
2
2
2 2
2 2
2 2
2 2
2
3
2
12, 4 5 2 0
13, 2 2
14, 4 6
8 15 9
15, 2 4 3
2
4 3 5
16, 2 2 5
2
17, 16 8 3 3 4
18, 10 6 2 1 2 2 4
12 12
19, 12
20, 2 1 1 0
1 1 1
21, 2 1 3
22, 4 1
x
x
x x x
x x
x x x
x x
x x
x x
x x
x x x x
x x x x x
x x
x x
x x x x x x
x
x x
x x x
+
=
− + + =
= − +
+ = +
− +
= − +
− −
= − −
− − = + −
− + = + − +
− + − =
− − − − + − =
−
+ = − + −
+
( ) ( )
( )
2
3 3
2 2 2 4
2
2
3 1 1
3 1
23, 3 1 2
1 3
24, 2 2 1 1 3 1 1
25, 4 2 1 3 5 1 1
26, 4 1 6 3 1 5 1
x x x x
x x
x x
x x
x x x x
x x x x
x x x x
= + − + −
− −
− + − =
− −
+ − − = + + −
+ − + = + + −
− − = − − + +

4
( )
( )
( )
( )
( )( )
2
2
32
2
2
2
2
2
2
2
2
1, 5 7 2 1
2, 9 10 4 4 1 0
3, 3 2 1 1
4, 5 1 1 4
5, 3 1 2 1
6, 20 4 5 2
7, 4 7 8 3 15
8, 10 3 2 1 13
9, 1 1 1 2 0
10, 5 1 11 4 1 0
11, 3 1 16 1
12, 1 3 2 1 2 1
13, 3
x x x
x x x
x x x
x x x x
x x x
x x x
x x x
x x x x
x x x
x x x x
x x x
x x x x
x
+ + = +
− + + − =
+ + + =
= + + +
+ = −
− + + =
+ + + =
+ + + =
− + + + >
+ + + − =
+ < + −
+ + ≥ − +
−( ) ( )
( )
( )
( )
( )
2
2
2
32
2
2
2
2 2
2 2
1 2 1 3 0
14, 16 5 1 1
5
15, 25 2 3 13
4
16, 3 11 3 4 3
17, 16 2 1 2 1
18, 40 7 2 14 1
2 1 7
19, 4 3 4
2 2
20, 2 3 3 9 20
21, 9 12 2 8 3
22, 4 11 10 1 2 6 2
23, 8 8 3 8 2 3
x x x
x x x
x x x
x x x x
x x x
x x x x
x
x x
x x x
x x x
x x x x x
x x x x x
+ + + + =
− = + +
+ + = +
≥ + + +
− − = −
+ = + −
+
+ = +
+ = + +
+ = + +
− + = − − +
− + = −
( ) ( )
( )
3 2 2
4 4 2 2
2 4
2 2
2 2
2 2
1
24, 2 2 6 1 2 2
2002 2002
25, 2002
2001
26, 4 2 2 4 1
27, 2 5 3 4 5 3
28, 2 2 3 4 2
29, 3 4 5 3 11 25 2
x x x x x x x
x x x x
x x x
x x x x x
x x x x
x x x x x
+
− + − = − − +
+ + +
=
− + = +
+ − = − −
+ − > − + +
+ − + − ≤ + +

5
( )
( )
( )( )
( )
( ) ( )
( )
2
2 2
2
2
2 2
2
2
2
2
2
1, 5 2 2 3 2 1 2 6
5
2, 6 1 2 1 4 1
2
16 2 19
3, 1 3
8
4, 16 24 3 26 47
5, 3 16 2 1 3 2 4 26
6, 2 3 3 29 46
7, 5 7 4 1 0
8, 5 2 2 1 4 2 2 3 1
9, 6 1 5 3 31 25
3 1 3
10, 1
2 1
x x x x
x x x x
x x
x x
x
x x x x
x x x x x
x x x x
x x x x
x x x x
x x x x
x x
x
− + + + =
= + + + +
+ −
≤ + +
+ + = +
+ + + + + =
+ ≤ − +
− + + =
< − + + +
+ + + = +
+ −
> +
−
( )
( )
( )
( )
2
2
2 2
2 2
2
2
2
2 2
2 2
2
11, 1 3 2
12, 48 6 2 19 23
13, 9 20 1 10 24
14, 4 5 2 2 3 1 2
15, 11 13 4 5 1
16, 2 1 4 2 18 42
3 59
17, 6 6
3
18, 6 17 3 2 2 2 3
19, 4 5 7 3 7 1 0
20, 11 8 2 1
x
x x
x x x x
x x x
x x x x x
x x x x x
x x x x
x x
x x
x
x x x x x
x x x x
x x x
− = − +
+ + + =
+ − > +
+ + + − + =
+ = − +
− = + − +
− +
≤ − +
−
+ = + − − +
+ + + + − =
+ > +( )
( )
( ) ( )( ) ( )
( ) ( )( )
( )
( )( )
2
2
2
2
2
6
21, 2 12 2 1 3 15
22, 7 37 26 6 3 1 0
23, 4 3 1 23 26
24, 21 83 12 6 7 50
25, 1 2 8 2 3 2
26, 4 2 1 2 3 8 11
27, 56 253 18 1 3 4 3 5 188 0
22 61 6
28, 1 2
6 3
x
x x x
x x x x
x x x
x x x x
x x x x
x x x x x
x x x x x
x x
x x
x
+
+ + + = −
+ + + − =
+ ≤ −
− + + ≥
+ = + − −
− + + + + = +
− + − − − + =
+ −
> − −
−

6
( )
( ) ( )( )
( ) ( )( )
( )
2 2
2
2
2 4 2
2 3 2
2 2
2
2
3 2
1, 2 1 1 23 18 4
2, 41 317 567 14 2 3 4
3, 4 8 6 2
4, 7 1 4 1
5, 5 2 4 3 1
6, 3 4 15 2 2 2 5
4
7, 3 3 3 4 1
8, 2 3 3 1 2 1 3
9, 49 211 20 3 7
10, 8 2 4
x x x x
x x x x x
x x x
x x x x
x x x x x
x x x x
x x x x
x
x x x x x
x x x
x x x
− − = − +
− + = − − −
+ < +
− + = + +
+ + = + + −
− ≤ + − −
 
− + ≤ − + − 
 
− = + + − −
+ = + +
− − =
( )
( )( )
( )
( )
2
2
2
2
2
2
2
2 2
2
2
2
2
8
11, 51 2 3 58 100
1
12, 1 7
1
13, 2 9 2 2 3 4 1
14, 3 3 3 4 1
15, 20 52 53 2 1
16, 6 4 1 3
17, 2 1 4 6 2
18, 2 4 6 7
27 4 5
19, 1
13
20, 4 13 6 5 1 4
21, 2 3 9 3
x
x x x
x
x x
x
x x x x x
x x x
x x x
x x x
x x x x
x x x x
x x
x
x x x
x x x x
−
− = − +
−
− + ≥
+
− + − − =
+ = + −
+ + = −
− + = −
− − + = +
− + − = − −
+ + +
≥
− + − =
+ ≥ +
( )
( )
( )
( )
2
2
2
2
2
2
2 2
2
2
22, 8 1 6 26 9 3
23, 11 31 4 1 0
24, 9 28 18 4 3 2 0
2 11 20
25, 3 1
12
26, 9 11 6 1 5 2
27, 5 12 1 2 8 1 3
28, 4 2 7 2 3 5 23 53
29, 2 5 9 9 8
x x x x
x x x
x x x
x x
x
x
x x x
x x x x
x x x x x
x x x x x
−
+ + = +
+ + + + <
+ + + + =
− −
≤ −
− = + −
+ + = +
+ + + + = +
+ + + = +

7
( )
( )
( )
( )( )
( )
( )
2
2 2
2 2
2
2
3 2 2 2
3 2
2
2
2 2 3 2
1, 16 44 21 2 5 4 4 5
2, 8 5 8 2 8 0
3, 6 15 7 2 3 1 3 1
5 6 2
4, 1
7 2
5, 6 8 14 8 3 7 4 3 2
2 5 10 12
6, 1 3
2 12
7, 6 31 6 3 5 1 6
8, 3 2 6 9 12 17 3
9, 3 2
x x x x
x x x x
x x x x x
x x
x
x
x x x x x x x
x x x
x x
x x
x x x x
x x x x x
x
+ + = + +
+ + + + − =
+ + + + + +
+ +
< +
+
+ + + < + + + +
+ − −
= − +
− −
+ + = + +
+ − − + + ≤
−
( )
( )
( )
( )
2
2
2
3 2 2 2
4 2 3
2 2
2 2
2
2
2
2
4 22 21
1
10, 2 4 1 4 4
11, 7 8 4 6 3 0
12, 8 6 3 6 5 2 1 2 2 1
13, 3 2 1 2 1 2 1
14, 3 5 6 2 3
15, 1 3 1 3 2 1
4
16, 3 6 2
3
1 2 1
17,
13 1 17 22 9
4 17
18,
x x
x x x
x
x x x x
x x x x x x x
x x x x x
x x x x x
x x x x x
x
x x
x x
x x x
x
+ + =
+ + = − +
+ + + + + >
− − + = − − − −
− − + = − +
− + = + −
− + + + + =
+
< − −
+ +
≥
+ + +
+
( )
( )
( )
( )
2
4 2
2 4 2
2 2 4 2 2
2 2 3 2
2 2 2
2
2
15
3 5
5 7
19, 2 4 3 10 6
3
20, 4 6 1 16 4 1 0
3
21, 2 1 1 3 1 1
22, 2 6 9 3 12 17 3 0
23, 1 1 8 6 1 10
24, 2 3 5 2 2 2
25, 12 2 2 1 3 5
26, 5 39 12
x
x x
x
x x x
x x x x
x x x x x x x x
x x x x x
x x x x
x x x x x
x x x
x x x x
+
= + +
+
+ ≤ − +
− + + + + =
− + − + + + + + = + +
− − + + + − ≥
+ + − − =
+ < + + + − +
+ + + ≥ +
− + + 3 2=

8
( )( )
( )
( ) ( )
( ) ( )
( )
( )( )
( )( )
( )
2
2 2
2 2
2 2
2
2
2 2
2
2
2
2
1, 7 1 3 7
31
2, 10 2 3 1 2 6 7
4
3, 2 1 3 4
4, 2 2 1 4 3 3 1 0
7 3 2
5, 2 1
7 1
6, 1 4 2 2 4 1
3 3 6 8
7, 4 5 6
1 3
9 26 24
8, 4 1 6
1 3
6 3 21
9,
6 58 173 1 1
6 3
10,
x x x x
x x x x x
x x x x
x x x x
x x
x
x
x x x x
x x
x x
x
x x
x x
x
x
x xx x
= − − + +
+ − + + + =
= + + +
+ + + + + =
+ −
< −
+
+ + = − + +
+ +
+ + ≤
−
+ +
= + +
−
−
≤
− +− −
−( )
( )
( )( )
( )( ) ( ) ( )( )
( )( )
( )
2 2
2
2
2
2
2
2
2 2
2
2
2
2 1
6 31 17 3 1
11 16 1
11, 1 4 1
4
12, 6 7 1 6 2 3 8 14
13, 1 2 2 3 2 1 1 9
7 27 25
14, 2 1
2 6
18 51 20
15, 6
2 1 2 5
16, 26 17 6 5 3 2
42 15 1
17, 4
3 2
18, 6 6 1
x
x x x x
x x
x x x
x x x x x
x x x x x
x x
x x
x
x
x x x
x x x x x
x x
x
x x
x x
≥
− + − +
− +
≤ − + +
− − + + + =
+ + + − + − =
− +
≤ − −
−
− −
=
− − +
− + + + =
− −
≥
+ +
+ +
( )
( )( )
( ) ( )( )
( ) ( ) ( )
( )
( )
2
2
2 2
2
59 17 15
1 3
19, 6 6 1 8 12 7
9 1 2
20, 2
3 4 5
21, 2 3 1 5 2 9 2 3
1 2 2 1 3 2
22, 1
2 1
x x
x
x x x x
x x
x x x
x x x x
x x x
x x
− −
<
−
+ − + − =
− + +
≤
+ + +
− + − + = +
+ + −
<
−

9
( )
( )
( )
( )
2 3 2
3 2
2 3
2
2
2
2 2
2
22 2
2
2
3 2 2
1, 6 4 2 11 2 2
2, 4 3 1 2 11 2 2 1
3, 10 13 7 17 1
4, 6 10 13 2
5, 2 2 1 2 4 1
4
6, 27 18
3
1 10 3 8
7,
4 1 32 1 1
8, 2 6 4
3 3 1 1 2 1 1
9,
2 1 2 1
10, 1 1
x x x x x
x x x x x
x x x
x x x
x x x
x x x
x x x
xx
x x x
x x x
x x x x
x x x
+ = + − + −
+ + = − + −
+ + = −
+ = − +
+ + = +
+ = +
− − −
≤
+− +
+ = − +
− − −
+ = +
− −
+ + −
( )( )
( ) ( )
( )( )
2
2 2
2
2
2
2 2
2
2
2
2
4 2 3 2
3 2
1 1
1 1
11, 2
2 4
12, 5 1 2 1 2 7 2
10 3 6
13, 2 2 1
3 1
14, 4 12 2 2 4 5
15, 11 1 11 1
16, 1 3 2 1
2 3
17, 5 2 1
3
18, 2 3 1 4
19, 8 33 9 13 3 0
20, 7 11 25 12
x x
x x x
x x x x
x x
x
x
x x x
x x x
x x
x x
x x
x
x x x x
x x x x
x x x
= − −
+ + + + =
− + + > + +
+ −
− ≤
+
− − = +
+ + <
+ = + +
− −
+ + − <
−
+ − = + −
+ − + + =
− + −
( )
2
2
2 4 3 2
2
2
2
2
1
3
2 2
21, 51 2 3 58 110
22, 18 13 2 3 81 108 56 12 1
4 11 10
23, 6 10
4
2
24, 5 4
1
3 7
25, 2 7
2
x
x
x x x
x x x x x x
x x
x
x
x
x
x x
x x
x
≥ − −
− = − +
− + = − + − +
+ +
= +
− <
−
+ +
= + +
+

10
( )( )
( )
( )
( )
( )
2
2
2
2
2
2
2
2
2
2
2
2 2
2
2 2
2 4
1, 2 5
2 4
4 2 1
2,
4 4 4 3 1
3, 2 1 4 4 2 1 4
10
4, 2 2 1
6 4
1
5, 8 4 3
22 4 2
2 1
6, 3 1 1
2 1
7, 23 4 1 5 9
2
8, 3 3 2 1 0
9, 12 2 2
x x
x
x
x x x
x x
x x x x x
x
x x
x
x
x x x
x
x x
x x x
x x
x x x
x x x
x
x x x x
− +
> −
−
− + −
>
− − +
+ − + = − + + +
−
+ ≤ − +
+ +
= + − + −
+ +
+ +
+ + + + =
+ + +
+ + − = +
 
− − + + + = 
 
+ + + − +
( )
( )
( )
( ) ( )
2
2 2
3 2
3 2 2
3 4 2 2
2
2
2 2
2
2
8 1
10, 4 2 3 1 8
1
11, 2 3 2 1 1 0
12, 10 3 1 1 6 3
13, 3 4 4 1 0
14, 10 6 4 7 1 2 2
15, 4 3 4
16, 20 4 2 4
17, 1 4 1 3
18, 2 3 1
1
19, 1 3 2 1
2
20, 3
x
x x x
x x
x
x x x x
x x x x
x x x x
x x x x
x x x x
x x x x
x x x x
x x x
x
+
+ + > +
 
− + − + ≤ 
 
+ + = + +
+ − − + ≥
− − ≤ − −
− = − −
+ + + = +
+ + + + ≥
− + ≤ +
− + = −
− ( )
( )
( )
2
2
2 2
2 2
2 2 2
3 2
2
10 6 2 2 0
21, 8 3 1 22 7
22, 4 4 2 3 6 4
1 5 1
23, 2 0
1 2 1
24, 4 1 4 2
25, 3 2 2 2 3
x x x
x x x x
x x x x
x x x
x x x x
x x x
x x x
+ + + − =
− + − + =
+ + > + −
 −
+ + + + = 
 − − 
− = + −
− = + −

11
( )( )
( )
( )
2
2
2 2
4 3 2 2
34 2 3
2
2
2
4 3
2
6 1
1, 1
2 3 4
2, 1 2 1 2 2
3, 2 2 1 1 6 1
4, 4 6 4 2 10 2
5, 8 33 9 13 3 0
6, 4 2 20 2 11 2 3
28
7, 64 4
3
5 14 11
8, 3 5
4 5
9, 40 52 8 4 15
10, 4 21 3 17 4
x x
x x
x x x
x x x x
x x x x x x
x x x x
x x x x
x
x
x
x x
x
x
x x x x
x x
− − −
>
+ − −
+ + − − ≥
+ + ≤ + +
+ + + + + + >
+ − + + =
= + + − +
−
− + ≤
+
− +
= −
−
− + = − +
+ = −
( )
( )
( ) ( )
( )
2
3
2
2 2
2
2
2
2
2
5
11, 1 90
2
12, 3 7 2 3 1 4 3 1 4
21 13 2
13, 3 1
4
5 9
14, 1
4 3 1 2
2
15, 4 3 1 7
35 5 2 5 1
16, 1
29
17, 8 11 2 2 5 1 0
18, 3 3 2 1 5 1 0
19, 8 1 2 3 1 2 0
8 9
20, 2 1
3
x
x x
x x
x x x x x x
x x
x
x
x x
x x
x
x
x x x
x
x x x x
x x x x
x x x x
x x
x
+
+
− + = +
+ − + + = + + −
− +
≥ −
−
=
− −
− = −
+ + −
<
− + + − =
− + + − =
− + + − − =
− +
= −
−
( )
( )
2
2
2
2 2
2
2
2
6 21 30
21, 11 3
2
1 11
22, 1
1 9
23, 6 4 1 2 1 3 1
13 10 1
24, 3 1
2 1
x
x x
x
x
x x
x x
x
x x x x
x x
x
x
− +
≥ +
−
− +
< + +
−
− + = − −
+ +
= −
−

12
( )
( )
2 3
2 3
2
2
2 2
2
2
2
2
2
2 2
2
2
1, 1 3
2, 3 2 4 2
4
3, 4 4 12
4
4, 4 5 1
8 4 1 3
5, 1
6, 2 1 1 4 5 1
3 1 4
7, 1
4 9 1 2
10 18
8, 2 4 2
10 19 1
9, 6 7 2 4 2 1
3 8 7
10, 3 2
1
1
x x x x
x x x x
x x x
x
x x
x
x x
x x
x x x x
x x x
x x
x x
x x
x x
x x x x
x x
x x
x
+ + > +
+ + = +
 
− + ≤ + 
 
+ = + −
+ − −
≤
+
+ + − = + −
+ + + −
≤
+ + −
− +
+ − − ≤
− + +
+ + = −
+ +
> + +
−
( )
2
2
2
2 2
2
2
2
2
2 2
2
2
2
17 16 5
1, 5 1
2 1
2
12, 7 3 5 3 2
13, 5 1 4 1 23 24 23
43
14, 9 2 0
4
8 2 1
15, 7
5 6 5
16, 5
1 2 3 1
17,
8 9
8 5 1
18,
7 6 1
19, 8 3 4 3 2 5
6 5
20, 8
1
6 5
21,
x x
x
x
x x x
x
x x x x x
x x x
x
x
x x
x x
x x
x x
x
x
x
xx x
x x x x
x x x
x
x
− +
< +
−
− − ≥ − −
− − − + = − +
− + + − =
−
+ = +
− −
+ ≤
− − +
≥
−
−
>
− − +
− + − + =
− −
>
−
−
2
2 2
6 14
1
9
22, 6 3 5 6 14
x
x x
x x x x
+ +
≤
−
+ + − + =

13
( )( )
( )
( )
( )
3 3 6
2
2
2 4 2
2 2
2
3 3
2 2
2 4 3 2
2
3
2
1, 2 3 2 2 5 3 2
2, 2 6 1 3 1 6
3, 1 1 5 9 6
4, 3 1 3 1
5, 11 12 3 4 5
6, 7 14 8 2
7, 4 1 1 2 2 1
8, 4 4 10 8 6 10
9, 2 4 7 4 3 2 7
2 5
10,
21
3
11,
x x x x
x x x x
x x x x
x x x x
x x x x x
x x x x
x x x x
x x x x
x x x x x x
x x
x
x
− + − = − −
− + = −
+ + − = + +
+ = + + +
− + > − − +
− + = −
− + = + +
− − = − −
+ + = + + − −
+
≤
−
( )( )
( )
( )
( )
2
2
2
3
2
2 2
2
2 2 23
2 3 2
5 14
3 5
2
12, 5 2 8
5 6
13, 3
6
4
14, 2 3 2
5 3 1
15, 5
1 1
6
16, 2 2 5 3
2 4
17, 3 0
5 1
18, 5 1 3 3 4 2
2
19, 3
20, 2 2 2
6
21, 4 2 3
22, 2 2 3 5 3 3 2
2
x
x
x
x x x
x
x
x
x x
x
x x
x x
x x
x
x
x x
x
x x x x
x x
x
x x x x
x x
x
x x x x x
+ +
> +
+
+ = +
+
= +
+
+ − > +
+ +
≤
+ −
+ + = +
+
+ + =
+ +
+ = + + +
− = −
+ = − −
+ − = +
+ + = + + +
( )
2
3 2 3
2 2
10 8
3, 2
6 5
24, 4 4 4 1 5 10
25, 6 3 14 13 2 14
x x
x
x
x x x x x
x x x
+ +
≤ +
+
− + + + =
− = −

14
( ) ( )
( )
( )
( )( )
2
2 22 2 23 3
2
2
2 2
2
2
2 3
2 4 2
2
2
2 2
5 1 3
1, 1 1
2 2 4
8 3 3
2, 3
3 4
3, 5 29 7 30 57
3 1
4, . 1
10
5, 3 4 1
6, 3 5 1 7 1
7, 4 8 1 7 1
8, 1 4 2 4
6 11 2
9, 2
4 7 1
10, 21 25 2
x x x x x
x x
x
x
x x x
x x
x
x
x x x x
x x x
x x x x
x x x x x x
x x x
x x x x
x x
 
− + + + + = + + 
 
+ +
= +
+
− = − +
+ +
= −
− = − −
+ + > −
+ + = + +
+ + + + = +
− + −
=
− + − +
− +
( ) ( )
( )
( )
( )
( )
2
2 2
2
2
2 2
2
3
3 2
2 4
2
2
2 4 2
2
2 19 2 1
11, 1 6 1 1
12, 5 6 1 3 1 1 13
13, 7 4 4 1 0
2 1
14,
1 3 5 3
2
15, 5
4
16, 4 1 4 2
17, 3 2 6 3 4
18, 2 2 1 4 3
19, 3 3 2 2 8
20, 4 1 5 1
21, 5 17 5
x x x
x x x x x
x x x x
x x x
xx
x x
x
x x
x x x
x x x
x x x
x x x
x x x
x x
− = − − + +
+ + + = +
− − + + + =
− + + + =
+
=
+ +
+
≤
+
− > + −
+ + ≥ +
− + = −
+ − + =
+ < + +
+ +
( ) ( )
( )
2 2
2
3 2 2
2
2
2
2 13 1 16 2
3 1 2 1
22,
23, 2 2 6 1 2 2
2 4 3
24, 3
5 4
25, 3 5 2 9 22
x x x
x x
x x x
x x x x x x x
x x
x
x
x x x x
− − = + + −
− −
≤
+
+ + − = − − +
+ +
= +
+
− + − = − +

15
( )
( ) ( )
( )
( )
( )
( )
( )
3 2
2
2
2
2
2
2
2
2
3 2 3 2
1, 4 3 2 11 6
3
2, 1 2 1 12
1
1 3
3, 1 4
3 1
2 3
4, 1 4
3 1
3 2 3
5, 3
3 1
6, 3 1 2 1 4 1 1 0
7, 5 1 5 1 5 1 3 1
8, 1 3 2 7 8
9, 9 13 8 5 4 3 3 4
10, 2 2 3
x x x
x
x x
x
x x
x
x x
x
x
x x
x x
x
x
x x x x
x x x x
x x x x
x x x x x x x
x x
+ = + +
−
− + + =
+
+ −
− + =
− +
−
− − =
− +
+ +
+ =
+
+ + − − + + − =
− + − + + = −
− + + ≤ + +
+ + + = + + + +
+ + −( )
( )
2
2
2
3 2
2
2
2
2 2
2 2
4 2 4
2
2
2 1 2 5 3 1
11, 20 80 105 2 1 4 3 5
12, 12 8 8 28 2 22 40
2 3 1
13, 1
2
14, 20 80 125 2 1 4 3 6
15, 5 10 60 24 5
16, 5 4 3 18 5
17, 3 4 3 3 16
1 8
18,
31
19
x x x
x x x x
x x x x
x x x
x x
x
x x x x
x x x x
x x x x x
x x x x
x x
x x
+ + + + ≤
+ + < + + +
− + + = + +
+ − +
− + =
+
+ + < + + +
+ = + − −
+ − − − =
+ − + = +
− +
≥
+
( )
( )
( )
( ) ( )
2 2 3 2
2
2 3
2 3
2
2
2
, 2 6 9 3 12 17 3 0
20, 20 4 2 2
21, 7 4 6 4
22, 12 8 3 3
23, 13 2 3 2 3 42 0
24, 1 5 3 3 4
25, 7 5 5 10 2
8 13
26, 56 84 28
7
x x x x x
x x x x
x x x x
x x x x
x x x
x x x
x x x x
x
x x
− − + + + − ≥
+ + + ≤ +
− + = +
+ > + −
+ + + + =
− + = −
− + = +
+
+ + =

16
( )
( )
( )
( )
( )
2 3 2
2
2 2
2
2
3 2
2
2
2 2
2 2
2
1, 9 4 4 2 3 3 1
3 7
2,
2 2
3, 10 6 4 2 2 4
5 2 7
4, 4 3 2 1
1
5, 17 2 5 2 1 0
6, 2 2 1
3 9
7, 3
3 3
7
8, 2 49 2 3
7
1
9, 2
2 1 2 1
10, 1 2 3 1
11, 4 3 4
x x x x x
x
x
x x
x x x x x
x
x
x x x x
x x x x
x x x
x
x x
x
x x
x
x
x x
x x x x
x x
− + = + + +
+
+ =
+
− + > + − +
+
+ = −
+
− − + + + =
+ = + + −
+ +
+ =
+ +
+
− > −
−
+ ≥
− −
+ − + = +
− − =
( )
( )
( )
( )( )
( )
3 4 2
2
2
2 2
2
4 2 2 2
2
2
2
2
2
5 4 1
12, 1
4 3
13, 6 2 3 4 3
14, 1 2 2 3 1
15, 8 11 8
16, 6 3 1 5 1 3
17, 6 3 1 3 1
18, 2 2 1 3 9
19, 4 1 2 3 1 3 1
20, 4 8 1
21, 3 1 1 3 2 2
22, 2 1 2 1
x x
x x
x
x
x x x x x x
x x x
x x x
x x x x
x x x x
x x x x
x x x x x
x x x
x x x
x x
−
− −
− =
−
+ + + + = + +
+ + = +
+ = −
+ + = +
= + + +
+ + + + =
+ + − + = +
− = −
+ − − + = −
+ = +
( )( ) ( )( )
2
2 3 3
33
3
2
1
23, 1 2 2 1 2
2 1
24, 1 16
2
3
25, 3 3 2 0
2
26, 4 6
x x
x x x x x x
x
x
x
x
x x x
− +
+ − + − = − −
+
+ =
+ + =
+
+ = +

17
( )
( )
2
2
2
2
2 2
2
3
2
2
3 2
2
2
2
4
1, 2 4
2
4
2, 5 4 2
35 4
4 11
3, 9
2 3
4, 4 1 4 1
5, 3 8 4 3 5
6, 4
4
7, 2 7 9 7
8, 4 3 4 3
9, 10 2 2 2 3 23
3
10, 2 3 1 8
7
11, 8 3 6 8
12, 2 4 3 3 3
13, 2
x
x x
x x
x
x
x x
x
x
x x x x
x x x
x
x
x
x x x
x x x x
x x x
x x
x
x x
x
x x x x
x x x
+
+ =
+ + = +
+
+ +
> +
+
+ + = + +
− + = −
+ =
−
+ = + +
+ + = +
+ + + = +
+ + = −
+ + = +
+ = + −
−
( )
( )
( )
2
2 2
2 2
2
2
2
2
2
1 4 3 1 2 2 6
14, 12 2 1 3 1
2 3 4
15, 1 9
3
16, 4 3 1 4
17, 3 2 3 3 1 3
18, 3 4 3 2
19, 4 1 2 3 1 3 1
3 7 8
20, 8
4 2
21, 3 3 3 1
22, 6 2 4 4 1 8
9 9
23, 1
10
24,
x x x
x x x
x
x
x x
x x
x
x x x x
x x x x x
x x x x x
x x
x
x
x x x x
x x x
x x
x
x
+ + + = + +
+ − = +
+
+ = −
+ = + +
+ + = + +
+ + = + + +
+ + − + = +
+ +
+ =
+
− + = + −
+ − + = +
− +
= −
( )
2
2
9 2
8
2
25, 7 5 18 5
x x x
x
x x x x
− −
≤
−
− + = +

18
( )
( )
( )
( )( )
( )
3 2
3
2 2
2 2
2
2 2
4 3 2 2
4 3 2 2
2 2 2
4
1, 3 2 1 1 3
2, 9 10 2 3 3 0
3, 10 7 2 2 8
4, 3 5 4 8 2 2
5, 3 6 1 4
6, 12 6 4 2 1
7, 4 4 5 3 8 4 6 3 5
8, 4 8 5 3 4 1 3
9, 12 2 1 3 3 1
10, 2
x x x x x
x x x x
x x x x x
x x x x
x x x
x x x
x x x x x x
x x x x x x x x
x x x x x x
x x
+ + − − =
− + + − − =
+ ≥ − + − +
+ − = − +
+ = − +
+ = + −
+ − − + = + −
+ + + + = + + +
+ + + − = + +
+ ( )3 2 2 4 3
4 3 2
4 3 2
2
4 3 2 2
4 3 2
4 3
2
4 3 2
2
2 4
2
2
5 4 1 4 2 1
2 5 4 11
11, 2 9
2 2 3
12, 6 13 12 3 6
2 4 2 1
13, 2 1
2 2 1
24 24 12 3 1
14, 5 6 3 1
2 1
15, 7 5 2 7 1
3 2
16, 1
2
x x x x x x x
x x x x
x x x
x x
x x x x x x
x x x
x x x
x x
x x x x
x x x
x
x x x
x x
x
x x
+ + + = + + + + +
− + − +
≤ − + +
− +
− + = + − +
+ + +
= + − +
+ +
− + − +
= − +
−
+ + = +
− +
= +
+
( )
2
2
2
4 3 2 2
2
4 3 2
2
2 3 2
2
4 2 2
2 2
2 8
17, 1
4 2 3 4 1
18, 2 6 4 4 1
19, 2 3 2 6 4 4 4 1
3
20, 2 7 3 3 2
2
1
21, 2 3 1 4 3
22, 7 8 4 6 10 4
23, 4 16 12 2 8
24, 4 6 2 1 2 3
3
25, 2 6 3 2
x x
x x
x x x
x x x x x x
x x
x x x x
x x x
x
x x x x x
x x x
x x x
x x x x x
x
+ −
<
+ + −
+ + = −
+ + + + = + −
−
+ − + − + =
+ + = − + +
+ + = + + +
+ + = +
− = + +

+ + + + + = +

( )4 3 4 3 2
26, 8 16 8 3 8 1 2 4 3 1x x x x x x x x x

 

+ − + = + + − − +

19
( )
( )
( )
( )
( )
( )
4 3 2 2 2
3 2 3 2
2
2
2
2
2
3
3 2
3
3
2 3 2
4
1, 2 8 7 8 4 4 6 3 0
2, 9 13 8 5 4 3 3 4
2 3 4
3, 3 5 6
1 1 3
4, 3 2 5 2
1 6
5, 1 2 1
4 2 6 2
6, 10 11 1
3 2
7, 2 6 3
8, 8 1 2 4 3 1
9, 2 4 1 3
x x x x x x x x
x x x x x x x
x
x x
x x
x x
x x
x
x x
x x
x x
x x
x
x x x
x
x
x x x x
x
x
+ + + + + + + + + =
+ + + = + + + +
−
− + = +
+ − 
+ ≤ + 
 
= + +
− +
+ − ≤ −
−
+ =
− ≤ − + − +
+ =
( )
2
3
2 3 2 3
3
2
2
2 2
2
2
2 4 3 2
2 2
2 2
2
2
2
10 6
1 3
10, 1 6 2 3 5
1 1 1
11, 3 16 10 2
2 3 2
12, 1 2 4
13, 2 11 15 2 2
14, 2 2 2 8 8 24 11 15
1
15, 2 11 15 2 2
3 2
16, 5 2 2 6
17, 8 10 2 1 15
18,
x x
x
x x x x x
x
x
x x
x x x
x x
x x x
x
x x x
x x x x x x
x x x
x
x
x x x
x
x x x
x
− +
+
+ − + = −
−
+ ≥ + − +
+ −
− − =
+ + = +
− + = − + − +
+ + = +
+
− + +
− = − +
( )
2
2 2
3 2
2
2
2 2
13 16 6 2 3 0
19, 4 32 8 8 1 20
20, 7 11 4 5 4 1
2 4 3
21, 2 3
1
4 4
22, 1 1 2 3 7
x x
x x x
x x x x
x x
x x
x
x x x x x
x x
− + + + =
− − = +
− + = − +
+ −
≤ + +
−
 
+ − − + = + − 
 

20
2 3
2 3
2 3
2 3
2 3
2 3
2
2
2
2
1, 2 5 30 11 2 12
2, 2 14 5 2 12 0
3, 9 10 11 7 1
4, 12 11 13 8 1
5, 2 2 4 3 2
6, 4 16 5 4
1
7, 1 2 1
8, 3 4 4 4
1
9, 1 6 2 10 5 0
1 3
10, 18 6 1 7
11, 13 11 12 8
x x x x
x x x x
x x x
x x x
x x x x
x x x x
x x
x
x x x x
x x x
x
x
x x x
x
x x x
+ + = + +
+ + − + + =
+ + = −
− + = +
− + = +
+ + = +
+ + = +
+ − − ≥
− + + + =
+
+ + >
− + ≤
( )
( )
3
2
3
2
2
2
2
2
2 2
2
3
2 2
3
2 2
2 2
2
2
1
3 1
12, 4 12 5 5
1
13, 4 4 1
14, 2 1 2 2 1
15, 4 4 2 3 6 9
16, 5 2 1 4
18 5 1
17, 20 3 2 3
18, 4 4 7 4 4 7
19, 4 4 3 4 1 2
3
20, 3 2 3 1
1
21, 4 4
x
x
x x
x x x
x
x x x
x
x x x x
x x x x x
x x x x
x x
x x x
x
x x x x x
x x x x x
x x x
x
x x
x
+
+ +
+ + =
+ + ≤ +
+ + = +
− + − + =
+ + ≤ − −
+ +
− + =
+ + = + +
− + = − +
− + = −
− =
( )
( )
2
2
2
1
3
22, 3 2 1 4 5 2
2
23, 7 5 10 2 0
1 2
24, 6 2 1 1 7
x x x
x
x
x x x
x
x
x x x
x
−
+ − = −
−
+ − − =
−
− = −

E2 f8 bộ binh

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E2 f8 bộ binh