CREATED BY HOÀNG MINH THI; TRUNG ĐOÀN 1 – SƯ ĐOÀN 5 – QUÂN ĐOÀN BỘ BINH
1

CHUYÊN ĐỀ PHƯƠNG TRÌNH VÀ BẤT PHƯƠNG TRÌNH

BÀI TẬP GIẢI PHƯƠNG TRÌNH BẬC CAO (PHẦN 1) 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

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

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 2
3 140 0
34, 17 7 9 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
− + − + =
− + − + =
− + − + =
− − + =
− − − + =
− + − + =
− + − + =
− + − + =
− − − + =
−
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

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
− + − + =
− + − + =
− + − + =
− + − + =
− + − + =

− + − + =
− + − + =
− + − + =
− − − + =
− + − + =
− + − + =
− + − + =
− + − + =CREATED BY HOÀNG MINH THI; TRUNG ĐOÀN 1 – SƯ ĐOÀN 5 – QUÂN ĐOÀN BỘ BINH
3Bài 3. Giải các phương trình sau trên tập hợp số thực
(
)
(
)
(
)
(
)
( )( )( )( )
( )( )( )
( )( )
( )( )( )( )
( )( )
( )( )( )( )
( )( )( )( )

+ + + + =
− + + + =
+ + + =
− + + =
+ + + + =
+ − + + = −
+ + − − =
+ + + + + =
− − − − =
+ − − =
+ + + + = + +
( )( )
( )( )( )( )
( )( )( )( )
( )( )( )( )
( )( )( )( )
( )( )( )( )
( )( )( )( )
( )( )( )( )
( )
( )( )
( )
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

( )( )
( )( )
( )( )( )( )
( )( )( )( )
( )( )( )( )
( )( )
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

Bài 4. Giải các phương trình sau trên tập hợp số thực
(
)
(
)
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( ) ( )
( )
( ) ( )
( ) ( )
( ) ( ) ( ) ( )
3 3
3 3
3 3
3
4 4
4 4
4 4
6 6
6 6
3 3 3
4
4
3 3

x
− + − =
− + − =
− − − + =
− + − =
− + − =
+ + + =
− + − =
− + − =
− + + = +
− + =
+ − − =
+ − = −
+ + + − − =
( )( )
( ) ( )
( )
( )
( ) ( )
( ) ( )
( )( )
( )( )
( )
( )
( ) ( )
( )
( )
( )( )
( ) ( ) ( )
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
− + + =
− + − =
+ + + =
− − =
− + − =
− − + =
− − + =
− − − + =
− − =
− + − =
+ − + − = −
− + − = −
( ) ( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )( )
( )
( )
( )( )
4


Bài 5. Giải các phương trình sau trên tập hợp số thực
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

x x
x x
x x
x
x
+ −
+ + =
+ −
 
+ = +
 
 
   
+ = +
   
   
 
+ = +
 
 
+
+ =
+
 
+ = + −
 
 
+
+ =
+

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
 
= +
 
 
+ + + + + =
   
+ + + + + =
   
   
  

18, 1 3 39 0
1 1
19, 1 1 1 0
1 3
20, 1 3 1 5
x x
x x
x x
x x
x x
x x
x x
x x
=
  
− + + + =
  
  
  
− − + + + =
  
  
  
− − + − + =
  
  
  
− + + − =
  
  

2 2 5 4
2, 20
1 1 2 1
2 5 2
3, 0
1
1
4 7 1
4, 0
3 2
1 2
3 28 48
5, 0
12
3 4
1 1
6, 4 7. 3
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

− −
 
− +
 
+ +
 
( )
( )
( ) ( )
( ) ( )
2
2 2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
0
2
1 1 1

x x x
x x x
x x x
+
 
=
 
+
 
 
+ − −
   
− + =
 
   
+ − −
   
 
−
 
+ =
 
− −
 
−
−
 
− + =
 
− −

2
2
2
2
3
, 2
1
1
19 4 19 5 6 5
3
13,
2
19 5 19 5 4 5
2 2 5 2
14, 9 3
1 1 1
3 2 7
15,
3 3
3
1 19
16,
1 12
2 2
17, 4 4
2 1 1
2011 4 2011 2
18,
x x
x

+
+
+
+ =
−
−
− + − =
− + −
− − − −
( ) ( )
( ) ( )( ) ( )
2
2 2
012 2013 2012
2013
2011
2012 5 2011 2012 2011 2012
x
x x x x
+ −
=
− + − − + −
CREATED BY HOÀNG MINH THI; TRUNG ĐOÀN 1 – SƯ ĐOÀN 5 – QUÂN ĐOÀN BỘ BINH
7Bài 7.

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
+ +
+
=
− + −
+ =
− + − + − +
+ = + +
+ + + +

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 8
15,
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 x
+ =
− +
+ + =

2
2 2
10
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
1 3
2 3 2
21, 0
3 3 5 3 63
x x x
x x
x x x x
x x
x x x x
x x x x
x x x x

8

Bài 8.
Giải các phương trình sau trên tập hợp số thực
(
)
(
)
( )( )
( )
( )
( )
( )
( )
3 2
2 2 2
3 3
3
2 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

= +
( )
( )
4 2
4 3
8 4
4 2
3
3
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, 7 3 3 1
18, 2 5 3
19, 1 0
20, 4 3
21, 4 1
22, 3 1 0

+ − − =
+ = +
−
( )
( )
( )
( )
( )
( )
5 4 3 2
8 5 2
2
2
3
3
2
2
2 3
2
2
2
4 2
3 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
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2 2
2 2
3
3
2
2 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
+ =
+
+ =
+
+ =
+
+ =
+
+ =
−
+ − + + =
   
+ =
   
+ −

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
− − + − =
+ + + − = −
+ + − + + + =
− + =
− − + =
− + = +
= + +
− + =
− = +
+ + + + =
−

− = +
+ + + =CREATED BY HOÀNG MINH THI; TRUNG ĐOÀN 1 – SƯ ĐOÀN 5 – QUÂN ĐOÀN BỘ BINH
10

Bài 10.
Giải các phương trình sau trên tập hợp số thực
(
)
(
)
( ) ( )
( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( ) ( )
( ) ( )
2
2 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
+ − + = −
+ − + + =
+ + = +
+ + = +
+ + = − + −
+ + + = +
− + = + + +
+ = + − + −
+ + + + =
+ + = + +
( ) ( )
( )
( )
( )
( )
( )
( )
( )
( ) ( )
( )( )

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 x x x x
− + + + + + =
+ + = +
+ + = +
+ + = + −
− − − + + − =
−
 
+ =
 
− −
 
−
+ =
− −
− −
+ + + + = + +
( )

2 3
4 2
4
2 3
4
4 2 2
, 1 4 1 5 5
20, 2 1 5 6 4
21, 3 1 3 7 13 10 2 0
22, 6 5 4 4 3 7 12 22
23, 18 2 1 9 4 4 27 9
24, 2 14 2 1 9 5 2
25, 3 15 2 6 1 8 2 19 3
26, 7 2 1 8 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
+ + + − + =
− = − − −
− − + + − =
− + = − + −
− = − − +
− + + − = − +
− + + − = − +
+ + + = +