E1 f4 bộ binh

CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH1
CHUYÊN ĐỀ PHƯƠNG TRÌNH – BẤT PHƯƠNG TRÌNH ĐẠI SỐ
PHƯƠNG TRÌNH HỮU TỶ QUY VỀ PHƯƠNG TRÌNH BẬC HAI
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Bài 1. Giải các phương trình sau trên tập hợp số thực
3 2
3 2
3 2
3 2
3 2
3 2
3 2
3 2
3 2
3 2
3 2
3 2
3
1, 4 2 1 0
2, 7 7 1 0
3, 9 7 1 0
4, 6 3 4 0
5, 5 8 12 0
6, 6 3 10 0
7, 7 14 8 0
8, 8 20 28 10 0
9, 3 4 4 0
10, 5 7 0
11, 13 42 36 0
12, 10 31 30 0
13,
x x x
x x x
x x x
x x x
x 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
4 3 2
4 3 2
4 3 2
4 2
4 2
4 3 2
4 3 2
4 3 2
4 3 2
7 2 0
14, 2 11 2 15 0
16, 5 3 6 0
17, 11 6 8 0
18, 10 25 36 0
19, 9 24 16 0
20, 16 40 25 0
21, 2 2 1 0
22, 3 13 10 0
23, 4 1 0
24, 2 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
+ − + =
− + + =
+ − − + =
+ − + + =
− + − =
− − − =
− − − =
− − − + =
+ − − − =
+ − + + =
+ − + +
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
2 0
25, 7 14 7 1 0
26, 10 1 0
27, 2 3 10 3 2 0
28, 3 4 8 4 3 0
29, 2 2 7 2 9 0
30, 10 26 10 1 0
31, 3 17 31 23 6 0
32, 2 27 118 183 90 0
33, 6 53 114 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
=
− + − + =
+ − + + =
− + − + =
− − − + =
+ + − − =
− + − + =
− + − + =
− + − + =
− + + 3 140 0x − =

Bài 2. Giải các phương trình đối xứng trên tập hợp số thực
4 3 2
4 3 2
4 3 2
4 3
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
4
1, 9 6 25 8 16 0
2, 9 6 16 8 16 0
3, 9 6 9 8 16 0
4, 9 6 8 16 0
5, 9 6 24 8 16 0
6, 9 6 21 8 16 0
7, 9 9 26 12 16 0
8, 9 12 27 16 16 0
9, 4 3 9 3 4 0
10, 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 x
x x x x
x
− + − + =
− + − + =
− + − + =
− − + =
− − − + =
− + − + =
− + − + =
− + − + =
− − − + =
− 3 2
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
4 2 2
4 2 2
4 3 2
4 3 2
8 7 1 0
11, 5 12 5 1 0
12, 6 5 38 5 6 0
13, 4 6 4 1 0
14, 7 16 7 1 0
15, 2 2 2 1 0
16, 6 10 6 1 0
17, 7 12 7 1 0
18, 8 14 8 1 0
19, 9 16 9 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
+ − + =
+ − + + =
+ − + + =
− + − + =
+ − + + =
− + − + =
− + − + =
− + − + =
− + − + =
− + − + =
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
4 3 2
0
20, 7 10 14 4 0
21, 5 8 10 4 0
22, 7 14 14 4 0
23, 5 10 10 4 0
24, 6 12 16 4 0
25, 9 18 18 4 0
26, 4 10 16 15 9 0
27, 4 12 30 18 9 0
28, 4 16 20 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
− + − + =
− + − + =
− + − + =
− + − + =
− + − + =
− + − + =
− + − + =
− + − + =
− + −
4 2 2
4 2 2
4 2 2
4 2 2
4 2 2
4 3 2
4 3 2
9 0
29, 4 16 19 24 9 0
30, 4 16 27 24 9 0
31, 4 16 28 24 9 0
32, 4 16 8 24 9 0
33, 4 16 3 24 9 0
34, 9 15 28 20 16 0
35, 9 12 12 16 16 0
x x x x
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
1, 1 2 3 4 120
2, 1 2 3 6 160
3, 1 2 3 9
4, 3 2 3
5, 5 6 8 9 40
6, 2 3 8 12 36
7, 2 3 7 8 144
8, 1 3 5 7 15 0
9, 4 5 6 7 1680
10, 2 2 10 72
11, 2 4 2 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 x x x x
+ + + + =
− + + + =
+ + + =
− + + =
+ + + + =
+ − + + = −
+ + − − =
+ + + + + =
− − − − =
+ − − =
+ + + + = + +
( )( )
( )( )( )( )
( )( )( )( )
( )( )( )( )
( )( )( )( )
( )( )( )( )
( )( )( )( )
( )( )( )( )
( )( )( )
( )
2 2
2
2 2
7
12, 3 4 6 24
13, 5 6 7 8 3024
14, 5 6 7 8 416
15, 5 7 10 8 2800
16, 2 5 3 7 3 1 2 9 315
17, 2 3 4 4 2 1 3 36 0
18, 3 1 1 5 1 15 7 7 0
19, 2 1 2 3 2 4 9 0
20, 1 3 5 9
21, 3 2 9
x x x x
x x x x
x x x x
x x x 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
20 112
22, 6 5 10 21 9
23, 8 4 2 1 4
24, 4 5 6 10 12 3
25, 2 4 3 4 14
26, 2 3 1 2 5 1 9
27, 1 2 3 6 168
28, 1 4 2 8 154
29, 4 3 2 6 160
30, 2 8 3 18 70
x x x x
x x x x x
x x x x x
x x x x x
x 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
31, 3 1 4 1 30
32, 6 2 8 2 99
x x x x x
x x x x x
+ + + + =
+ + + + =

( ) ( )( )
( ) ( )( )
( ) ( )( )
( ) ( )( )
( ) ( )( )
( )( )( ) ( )
( )( )( )
( )
2
2
2
2
2
3 2
4
4
4
4 2
6 2
1, 4 3 1 2 1 810
2, 6 5 3 2 1 35
3, 12 1 1 2 1 1
4, 20 1 2 1 5 1 1
5, 8 1 2 1 4 1 1215
6, 3 3 4 5 8 2
7, 3 5 6 7 8
8, 2 2 2 2 2 0
9, 8 7
10, 8 3 4
11, 4 1
12, 10 25
13, 7 6 0
14, 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
+ + + =
+ + + =
+ + + =
+ + + =
+ + + =
+ + + = −
+ + + =
+ + + =
= +
= +
= +
− + =
− + =
( ) ( )( )
( ) ( )
( )( )( )
( )
( ) ( )
( )( )
( )( )( )( )
( ) ( )
( ) ( ) ( )
( )
2
22 2
2
4 2
22 2
4 2
4 3 2
4 22 4 2 2
2 3 4
4
8 7 4 3 1 7
15, 5 10 5 24
16, 3 1 1 2 6
17, 9 5 3
18, 6 9 4 9
19, 1 5 6 6 0
20, 6 5 38 5 6 0
21, 4 1 12 1 3 2 1 4
22, 1 5 6 1
23, 2 2 2 2
24, 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
+ + + =
− + − =
+ + + + =
+ = −
− − = − −
+ + − − =
− − − + =
+ − + + =
− + + = − +
+ + + + + =
+ = ( ) ( )
( ) ( )( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )
3
22 2
2 22 2
3 3 3
3 3 3 3
2
4 3 2
2 2 13 50 2 13
25, 1 2 3 4 5 0
26, 1 1 2 1
27, 2 3 2 3 2
28, 1 5 1 27 1 5
15 1 1
29, 1 12
3 4 4 3 3
30, 2 9 14 9 2 0
x x
x 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 3
3 3
3 3 3
4 4
4 4
4 4
6 6
6 6
3 3 3
22
4 4
4 3 2
3
6 5 4
1, 2 4 8
2, 4 6 28
3, 5 7 133
4, 4 6 16
5, 2 4 2
6, 2 8 272
7, 2 4 64
8, 1 3 2
9, 1 2 2 1
10, 4 1 8
11, 1 97
12, 10 26 1 0
13, 2 4
14, 3 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
− + − =
− + − =
− − − + =
− + − =
− + − =
+ + + =
− + − =
− + − =
− + + = +
− = +
− + =
+ + + =
= +
+ + +
( ) ( )
( )( )
( ) ( ) ( )
( ) ( ) ( )
( )
3 2
2 42
2 2
2 22 3
24 42
4 3 2
4 2
5 4 2
5 4 3 2
6 5 4 3 2
7 6 3 1 0
15, 4 21 3
16, 6 5 10 21 9
17, 3 1 2 1 5 1
18, 3 6 2 2
19, 3 6 5 2 5 0
20, 2 8 4 0
21, 2 2 1 3 1
22, 2 3 3 2 1 0
23, 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
+ + + =
+ + = +
+ + + + =
− + = + + +
+ = + − + −
− + − − =
+ + − =
+ + + = +
+ + + + + =
+ + + + + + =
( ) ( ) ( )
( ) ( )
( ) ( )
( ) ( )
5 4 3 2
4 3 2
2 22 3
4 2 2
22 2 2
4 3 2
22 2 2
22 2 2
0
24, 6 29 27 27 29 6 0
25, 2 21 74 105 50 0
26, 2 1 7 1 13 1
27, 3 2 6 4 0
28, 2 2 5 2 2
29, 4 3 14 6 0
30, 2 3 2 2 0
31, 1 3 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
− + + − + =
− + − + =
+ + = − + −
+ − − + =
+ − + = −
+ − − + =
+ − + + =
+ + = +

( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( )( )
( ) ( )
( )( )
( )
( ) ( )
( ) ( )
3 3
3 33
2 2
2 2
4 3 2
5 4 3 2
22 4 2
2
22
22 2 2
4 2
1, 3 1 56
2, 1 2 1
3, 1 2 1 2 12
4, 1 4 3 192
5, 3 4 3 1 0
6, 3 3 1 0
7, 1 3 1
8, 1 1 12
9, 9 12 1
10, 1 3 1 2 0
11, 3 15 6 10 1
12, 2 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
+ − − =
+ − = −
+ + + − − =
− + + =
+ + + + =
− + + − + =
+ + = + +
+ + + =
− = +
+ + + + =
− − − + =
( ) ( )
( ) ( )( )
( )( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( )
( ) ( )
2
2
2 2
4 3 2
4 3 2
5 4 3 2
5 4 2
2 2 4
5 5
4 4
6
1 4 1 9
13, 12 7 3 2 2 1 3
14, 6 4 1
15, 6 25 12 25 6 0
16, 6 7 36 7 6 0
17, 2 3 3 2 1 0
18, 4 3 2
19, 7 8 15 2
20, 1 1 242 1
21, 2,5 1,5 1
22, 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
− − =
+ + + =
+ − + − = −
+ + − + =
+ − − + =
+ + + + + =
= + − +
− + − = −
− + + = +
− + − =
− + −
( )( )( )( )
( )( )( )
( ) ( )( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
6
2
22
2 22
2 22
2 22
2 22
2
22
1
23, 2 1 2 3 2 4 9 0
24, 1 3 2 2
25, 2 2 1 1 11
26, 2 4 2 4
27, 3 6 4 3 36
28, 10 5 5 125
29, 3 4 7 2 28 0
1 1
30, 2
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
=
− + + + + =
+ − − = −
− + + − =
− + − =
− + − =
− + − =
− − − + =
 
− + − = 
 

2
2
3
3
3
3
3
3
2
2
2
2
4 2
2 4
2 2
2
2
4
4
5 3
1, 4 0
5
1 1
2, 6
1 1
3, 4 13
1 1
4, 78
1 5
5,
1 2
1 1
6, 3 4
2 1
7, 2
2 1
6 6
8, 722
6
1 1
9, 10 6
1
10, 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
+ −
+ + =
+ −
 
+ = + 
 
   
+ = +   
   
 
+ = + 
 
+
+ =
+
 
+ = + − 
 
+
+ =
+
+
+ =
+
 
+ + = + 
 
+ + 2
2
3 2
3 2
3 2
3 2
2
2
2
2
2 2
2
2
1
2 7
1 1 1
11, 6
1 1 1
12, 3 5 16
1 1
13, 1 2
1 1
14, 3 1 3
1 1 40
15, 1
2 9
1 1 5
16, 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
 
= + 
 
+ + + + + =
   
+ + + + + =   
   
  
+ + − =  
  
  
+ − + + = −  
  
−   
− + =   
−   
  
− − + − +  
  
( )
2
2
2
2
2
2
4 2
0
8
1 1
17, 2 5 4 1 36
3 9
18, 1 3 39 0
1 1
19, 1 1 1 0
20, 1 2 3
x x
x x
x x
x x
x x
x x
x x x
=
  
− + + + =  
  
  
− − + + + =  
  
  
− − + − + =  
  
− + = +

Bài 12. Giải các phương trình sau:
( )
( ) ( )
( ) ( )
2 22
2
2 2 2
2
2
2 2
2
2 22
2
2 22
2
2 4 2
1, 20 48 5
1 1 1
2 2 5 4
2, 20
1 1 2 1
2 5 2
3, 0
11
4 7 1
4, 0
3 21 2
3 28 48
5, 0
123 4
1 1
6, 4 7. 3
1 2
x x x
x x x
x x x
x x x
x
x xx
x x
x xx x
x x
x xx x
x x
x x
 − − +   
+ =    
+ − −    
 + − −   
+ =     
+ − −     
− + =
−−
− + =
− +− −
− + =
+ −− +
− − 
− + 
+ + 
( )
( )
( ) ( )
( ) ( )
2
2 22
2
2
22
2 2
2 2
2 2
2 2
2
1
0
2
1 1 1
7, 3 8 5 0
3 9 3
4
8, 2
1 1
5 24 2
9, 0
1 11
3 2 3 1
10,
34 3 9 3 5
3 9 8 28
11, 7 2
5 25 5
12
x
x
x x x
x x x
x x
x x
x xx x
x xx
x x x x
x x x
x x x
x x x
+ 
= 
+ 
 + − −   
− + =    
+ − −    
− 
+ = 
− − 
− − 
− + = 
− − −
− − − +
=
− − − +
 + − − 
− + =  
+ − −   
( )
( ) ( )( ) ( )
( ) ( )( ) ( )
( )
( ) ( )( ) ( )
3 2
3
3
2 2
2 2
3 2
2 3
2
2
2
3
2 2
3
, 2
11
19 4 19 5 6 5 3
13,
219 5 19 5 4 5
2 2 5 2
14, 9 3
1 1 1
3 2 7
15,
3 33
1 19
16,
1 12
17, 9 6 0
2011 4 2011 2012 2013 2012
18,
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
x
+ + =
−−
− − − + + +
=
− + − + + +
− − −   
+ =   
− − −   
+ + −
− =
+ +
+
+ =
−
+ + =
− − − − + −
−( ) ( )( ) ( )
2 2
2013
20112012 5 2011 2012 2011 2012x x x
=
+ − − + −

( ) ( )2
2
2 2 2
2 2
2 2
2
2 2
2 2
2 2
2
9 1 7 1
1,
1 1
1 2 6
2,
3 3 3 4 3 5
1 1 21 1 1
3,
6 7 21 9 10
2 7
4, 1
3 2 3 5 2
3 7
5, 4 0
3 1 1
10 15 4
6,
6 15 12 15
3 5 1 5 5
7,
4 5 4 6 5
13
8,
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
+ + +
=
− + −
+ =
− + − + − +
+ = + +
+ + + +
= +
− + + +
+ + =
− + + +
− +
=
− + − +
− + − +
+ =
− + − +
+
( )
2
2 2
2 2
2 2 2 2
2 2
2 2
2
2
6
3 2 5 3
4 5
9, 1 0
8 7 10 7
3 2 8
10,
4 1 1 3
8 8
11, 15
1 1
1 6 2 5
12,
2 12 35 4 3 10 24
24 15
13, 2
2 8 2 3
2 13
14, 6
2 5 3 2 3
6
15,
x
x x x
x x
x x x x
x x
x x x x
x x x
x
x x
x 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
4 3 2
8
10
1 1
20 21
16, 13
3 4 3 4
3 5
17, 12
5 3 5
6 6
18, 5 0
5 6 8 6
3 1 25
19,
1 9 1 14
5 2 9 2 14
20,
2 3 2 3
21, 8 9 8 1 0
x
x x
x x
x x x x
x x
x x x x
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
3 332 2
4 4
4 3 2
4 3 2
3 2
4 3 2
4 3
4 2
4 2
1, 1 2 3 2 2 3 4 3
2, 3 2 7 12 5 6
3, 1 1 3 3 2
4, 2 1 27 12 12
5, 3 14 6 4 0
6, 4 3 12 16
7, 4 2 22 17 2 6
8, 2 2 1 0
9, 2 132
10, 3 10 4
11, 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
+ − + − =
+ + + + + + =
+ + − = − +
+ + + = +
− − − + =
+ + = +
− + =
+ + + + =
− + =
− − =
= +
( )
( )
4 2
4 3
8 4
4 2
33
3 2
3
3 2
4 2
4
4 3 2
3 2
3 2
7 6
8 3
12, 2 12 8
13, 3 3 1 0
14, 20 0
15, 12 16 2 12
16, 8 1 162 27
17, 3 9 9
18, 2 5 3
19, 1 0
20, 4 3
21, 4 1
22, 3 1 0
23, 9 18 0
24, 2 2 1
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
+
= − +
− + + =
− − =
− + =
+ = −
− + =
+ =
− + =
+ + =
= +
+ + + + =
+ − − =
+ = +
− +
( )
( )
( ) ( ) ( )
( )
5 4 3 2
8 5 2
22
3
3
2 22 3
2
22
4 2
3 3 2 1 0
26, 1 0
27, 3 2 3 2
28, 162 27 3 8 3
29, 3 1 2 1 5 1
1 1
30, 1 3
2 4
32, 2 3 3 3
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
22 2
2 2
33
22 2
22 2
4
1, 12
2
81
2, 40
9
3, 15
1
9
4, 7
3
5, 3
1
6, 3 4 3 8 16
7, 90
1 1
8 2001
8, 4004 2001
2002
9, 2 2 2 5 4 3 5 0
10, 8 15 9 2 2 4 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
+ =
+
+ =
+
+ =
+
+ =
+
+ =
−
+ − + + =
   
+ =   
+ −   
 +
= − 
 
− − − + + =
− + = − +
( ) ( )
( ) ( )( ) ( )
( ) ( )
3 2
2 22 2
22 2 2
4 2
4 3 2
4 3 2
2 4
4 2
4 2
4 3 2
4
, 3 2 1 2 1 0
12, 1 1 3 2 6 3 2
13, 1 6 1 5 0
14, 6 12 8
15, 6 22 10 1
16, 2 24 4 35
17, 21 10 3
18, 4 5 4 3
19, 9 8 1 12
20, 35 6 13 6 3 0
21, 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
− − + − =
+ + + − = −
+ + − + + + =
− + =
− − + =
− + = +
= + +
− + =
− = +
+ + + + =
− 3 2
4 3 2
4 3 2
4 2
4 3 2
4 3 2
4 2
8 1 15
22, 4 5 6 1
23, 4 4 3 1 4
24, 1 10 8
25, 10 9 24 9
26, 8 7 12 4
27, 3 4 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
+ = +
= + + +
− − = −
+ = −
− + + =
− + = +
− = +

Bài 16. Giải các phương trình trên tập hợp số thực
4 2
4 3 2
3 3 2
4 2
4 2
6 4 3 2
3
3
3
3
3
3
2
2
1, 10 4 8
2, 6 16 40 16
3, 4 32 12 1
4, 48 42 16
5, 13 24 12
6, 4 6 4 1 0
8 2
7, 4 6 0
8 2
8 2
8, 6 5
27 3
27 3
9, 6 4
27 3
1
10, 8 4 10
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
= − −
− = − +
− = − +
+ = +
− + =
− + − + =
 
+ − + + = 
 
 
+ + = + 
 
 
+ + = + 
 
+ + =
( )
4 3 2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
, 6 8 2 1
7
12, 7 7
1
13, 3 10 10
1
1
14, 2 2
1 4
15, 3 4 3
5 1
16, 3 4 4
4
17, 8 6 1
9 19
18,
41
1 7
19, 0
4
4 7
20, 3
4
41 1
21, 7
4
4 23
22, 8 5 0
4
23, 16
x x x x
x
x x
x
x x
x
x
x
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
24 4
6
14 24 3
24, 5
x
x
x
x
x
x x
−
= +
−
− = +

( )
( )
( )
( )
( )
( )
2 2
2 2
2 2
2 2
2
2
2
2
2
2
2
2
2
2
2
2
5 8
1, 5
1 4 1
4 4 5 5
2, 8
2 3
1 2 4 4 4
3,
11
1 5 11 4 1
4,
11
1 2
5, 3 2
1 4
6, 4 4 1
1 1
7, 3 1
1 5 9
8, 4 4 3
33
1 7 1
9, 9 6
11
9 6
10,
x x
x x x x
x x
x x x x
x x
x xx
x
x x xx
x
x
x x
x
x x
x x
x
x x
x x
x
x x
xx
x
x x
xx
x
x
+ =
+ + − +
− −
+ =
− + +
+ −
+ =
++
+
+ + =
++
+
+ = +
−
+ = + +
−
+ = + +
−
+ = + −
−−
+
+ = +
−−
+
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )( )
( )
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1 9 6
1 13 7
11, 9 6
11
1 16 10
12, 4 2
11
1 9 14
13, 2 3 5
22
1 4 10
14, 3 3
4 124 3
1 3 7
15, 1
4 124 3
2 2 6
16, 1 4 4 3
11
1 2 5
17, 7 36 12
2 11 2
1
18,
3
x x
x
x x
xx
x
x x
xx
x
x
xx
x
x x
xx
x
x x
xx
x x x
x x
xx
x
x x
xx
+ = +
+
+ = +
++
+
+ = + +
−−
−
+ = + +
−−
−
+ = + +
−−
−
+ = +
−−
− +
+ + = − −
−−
+
+ + = −
−−
( )
( )
2
2
2
2
2 3
7 16 8
2 32
1 24
19, 100 20 2
4 11 4
x
x x
xx
x
x x
xx
+
+ + = −
−−
+ = − +
−−

( )
2 2
2 2
2 2
2 2
2 2
2 2
2
2
4
2
5 5 6 6 17
1,
4 6 5 7 2
4 8 7 14
2, 1
10 18 4 6
9 10 1
3,
2 7 8 9 4 2
3 15 45 11
4,
2 13 22 4 15 47 2
4 7 5
5,
6 1 1 2
7 6 62
6,
7 1 8 1 45
6 5
7, 5
9
8, 2 3
33
x x
x x x x
x x
x x x x
x x
x x x 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
− −
+ =
− + − +
− −
+ =
− + − +
+ =
− + − +
− −
− =
− + − +
+ =
− + +
+ =
+ + + +
+
− =
+ + =
++
( )
( )
2
2
2
2
2
2
4 2
4 3 2
4 3 2
4 3 2
4 3
4 3 2
4 3 2
4 3 2
4 3
16
9, 4 17
2
36
10, 9 33 0
2
11, 1 9 6
12, 9 12 12 8 1
13, 9 30 16 6 1
14, 8 30 29 1
15, 9 30 10 1
16, 16 30 35 1 0
17, 4 10 37 14
18, 5 4 4 0
19, 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
+ =
+
+ + =
−
− = +
− − + =
− + + =
− + =
− + =
+ − + =
− − + =
− − + + =
− + 2
4 3 2
4 3 2
4
5 4 3 2
4 3 2
4 3 2
3 2
3 2
8 7 6 5 4 3 2
3 2 0
20, 32 48 10 21 5 0
21, 2 3 15 3 2 0
11 6
22,
6 11
23, 2 3 5 5 3 2 0
24, 12 32 8 4
25, 2 3 16 3 2 0
26, 6 1
27, 3 3 3 1
28, 2 9 20 33 46 66 80
x x
x x x x
x x x x
x
x
x
x x x x x
x x x x
x x x x
x x
x x x
x x x x x x x
− + =
− − + + =
+ − + + =
−
=
−
+ − − + + =
+ + = +
+ − + + =
= +
− − =
− + − + − + 72 72 0x− + =

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