E1 f4 bộ binh
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CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 1
CHUYÊN ĐỀ PHƯƠNG TRÌNH – BẤT PHƯƠNG TRÌNH ĐẠI SỐ
PHƯƠNG TRÌNH HỮU TỶ QUY VỀ PHƯƠNG TRÌNH BẬC HAI ------------------------------------------------------------------------------------------------------------------------------------------- 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 − =
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 2
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
+ =
− + − + =
− + − + =
− + − + =
− − − + =
− + − + =
− + − + =
− + − + =
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 3
Bài 3. Giải các phương trình sau trên tập hợp số thực
( )( )( ) ( )( )( )( )( )( ) ( )( )( )( )( ) ( )( )( )( )( )( ) ( )( ) ( )( )( ) ( )( )( )( )( )( )( ) ( )( )( )( )
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
+ + + + =
+ + + + =
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 4
Bài 4. Giải các phương trình sau trên tập hợp số thực
( ) ( )( )
( ) ( ) ( )
( ) ( )( )
( ) ( )( )
( ) ( ) ( )( )( )( ) ( )( )( ) ( )
( )
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 1 129, 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
+ + +
+ + + − − =
− + − = +
− + + = + −
− − − + = − −
− = + + − + −
− + − + =
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 5
Bài 5. 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
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
− + + − + =
− + − + =
+ + = − + −
+ − − + =
+ − + = −
+ − − + =
+ − + + =
+ + = +
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 6
Bài 6. Giải các phương trình sau trên tập hợp số thực
( ) ( )
( ) ( )
( ) ( ) ( ) ( )( )( )
( ) ( )( )( )
( )( ) ( )( ) ( )
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
222
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
1 130, 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
=
− + + + + =
+ − − = −
− + + − =
− + − =
− + − =
− + − =
− − − + =
− + − =
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 7
Bài 7. Giải các phương trình sau trên tập hợp số thực
2
2
33
33
33
2
2
22
4 2
2 4
2 2
22
44
5 31, 4 0
51 1
2, 6
1 13, 4 13
1 14, 78
1 55,
1 21 1
6, 3 4
2 17, 2
2 16 6
8, 7226
1 19, 10 6
110, 1
x x x
x x x
x xx x
x xx x
x xx x
x x
x x
x xx x
x x
x x
x x
x x
x xx x
xx
+ −+ + =
+ −
+ = +
+ = +
+ = +
++ =
+
+ = + −
++ =
++
+ =+
+ + = +
+ + 22
3 23 2
3 23 2
22
22
2 2
22
12 7
1 1 111, 6
1 1 112, 3 5 16
1 113, 1 2
1 114, 3 1 3
1 1 4015, 1
2 9
1 1 516, 4 4
xx
x x xx x x
x x xx x x
x xx x
x xx x
x
x x
x xx x
= +
+ + + + + =
+ + + + + =
+ + − =
+ − + + = −
− − + = −
− − + − +
( )
22
22
22
4 2
08
1 117, 2 5 4 1 36
3 918, 1 3 39 0
1 119, 1 1 1 0
20, 1 2 3
x xx x
x xx x
x xx x
x x x
=
− + + + =
− − + + + =
− − + − + =
− + = +
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 8
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 21, 20 48 5
1 1 1
2 2 5 42, 20
1 1 2 1
2 5 23, 0
11
4 7 14, 0
3 21 2
3 28 485, 0
123 4
1 16, 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
10
2
1 1 17, 3 8 5 0
3 9 3
48, 2
1 1
5 24 29, 0
1 11
3 2 3 110,
34 3 9 3 5
3 9 8 2811, 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 23
3
2 2
2 2
3 2
2 3
2
2
2
3
2 2
3, 2
11
19 4 19 5 6 5 313,
219 5 19 5 4 5
2 2 5 214, 9 3
1 1 1
3 2 715,
3 33
1 1916,
1 12
17, 9 6 0
2011 4 2011 2012 2013 201218,
x xx
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
=+ − − + −
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 9
Bài 13. Giải các phương trình sau trên tập hợp số thực
( ) ( )2
2
2 2 2
2 2
2 2
2
2 2
2 2
2 2
2
9 1 7 11,
1 11 2 6
2,3 3 3 4 3 5
1 1 21 1 13,
6 7 21 9 102 7
4, 13 2 3 5 2
3 75, 4 0
3 1 1
10 15 46,
6 15 12 15
3 5 1 5 57,
4 5 4 6 513
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
26
3 2 5 34 5
9, 1 08 7 10 73 2 8
10,4 1 1 3
8 811, 15
1 1
1 6 2 512,
2 12 35 4 3 10 2424 15
13, 22 8 2 32 13
14, 62 5 3 2 3
615,
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 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
810
1 120 21
16, 133 4 3 4
3 517, 12
5 3 5
6 618, 5 0
5 6 8 63 1 25
19,1 9 1 14
5 2 9 2 1420,
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
+ =+ − +
= −+ + − +
+= +
+ + + +− + + +
+ + =− + − +
+= +
+ − ++ + + +
+ =+ + +
− + − + =
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 10
Bài 14. Giải các phương trình sau trên tập hợp số thực
( ) ( )( )( )( ) ( ) ( )
( ) ( )
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
33
2 22 3
222
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
1 130, 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
− − + − + =
− + − + =
+ − =
+ = −
− + − + = +
+ + = + +
− + + =
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 11
Bài 15. Giải các phương trình sau trên tập hợp số thực
( )
( )
( )
( )
( )
( )
( )( )
22
2
22
2
22
2
22
2
22
2
22 2
2 2
33
22 2
22 2
41, 12
2
812, 40
9
3, 151
94, 7
3
5, 31
6, 3 4 3 8 16
7, 901 1
8 20018, 4004 2001
2002
9, 2 2 2 5 4 3 5 0
10, 8 15 9 2 2 4 3
11
xx
x
xx
x
xx
x
xx
x
xx
x
x x x x
x x
x x
xx
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
+ = +
= + + +
− − = −
+ = −
− + + =
− + = +
− = +
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 12
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
22
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 27, 4 6 0
8 2
8 28, 6 5
27 3
27 39, 6 4
27 3
110, 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 xx
= − −
− = − +
− = − +
+ = +
− + =
− + − + =
+ − + + =
+ + = +
+ + = +
+ + =
( )
4 3 2
22
2
2
2
2
22
2
22
2
22
2
2
2
2
22
2
, 6 8 2 1
712, 7 7
113, 3 10 10
1
114, 2 2
1 415, 3 4 3
5 116, 3 4 4
417, 8 6 1
9 1918,
41
1 719, 0
44 7
20, 34
41 121, 7
44 23
22, 8 5 04
23, 16
x x x x
xx x
x
x xx
xx
x
xx x
x
xx x
x
x xx
x
x
xx
xx
xx
x xx
x
− + + =
−− + =
− + =−
+− = +
+− + =
+− + =
− + =
− = +−
+ + =
− = +
= +
+ + + =
+2
2
22
2
24 46
14 24 324, 5
xx
x
xx
x x
−= +
−− = +
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 13
Bài 17. Giải các phương trình sau trên tập hợp số thực
( )
( )
( )
( )
( )
( )
2 2
2 2
2 2
2 2
2
2
22
22
2
22
22
2
5 81, 5
1 4 14 4 5 5
2, 82 3
1 2 4 4 43,
11
1 5 11 4 14,
11
1 25, 3 2
1 46, 4 4 1
1 17, 3 1
1 5 98, 4 4 3
33
1 7 19, 9 6
11
9 610,
x x
x x x x
x x
x x x x
x x
x xx
x
x x xx
xx
x x
xx x
x x
xx x
x x
xx x
xx
xx x
xx
x
x
+ =+ + − +− −
+ =− + +
+ −+ =
++
++ + =
++
++ = +
−+ = + +
−+ = + +
−+ = + −
−−
++ = +
−−
+
( )
( )( )
( )( )
( )
( )( )
( )( )( )
( )
2
22
22
2
2
22
2
2
2
22
1 9 6
1 13 711, 9 6
11
1 16 1012, 4 2
11
1 9 1413, 2 3 5
22
1 4 1014, 3 3
4 124 3
1 3 715, 1
4 124 3
2 2 616, 1 4 4 3
11
1 2 517, 7 36 12
2 11 2
118,
3
x x
xx x
xx
xx x
xx
xx
xx
xx x
xx
xx x
xx
x x xx x
xx
xx x
xx
+ = +
++ = +
++
++ = + +
−−
−+ = + +
−−
−+ = + +
−−
−+ = +
−−
− ++ + = − −
−−
++ + = −
−−
( )
( )
22
22
2 37 16 8
2 32
1 2419, 100 20 2
4 11 4
xx x
xx
xx x
xx
++ + = −
−−
+ = − +−−
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN BỘ BINH 14
Bài 18. Giải các phương trình sau trên tập hợp số thực
( )
2 2
2 2
2 2
2 2
2 2
2 2
22
4
2
5 5 6 6 171,
4 6 5 7 24 8 7 14
2, 110 18 4 69 10 1
3,2 7 8 9 4 2
3 15 45 114,
2 13 22 4 15 47 24 7 5
5,6 1 1 2
7 6 626,
7 1 8 1 456 5
7, 5
98, 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
xx
x
x xx
xx
− −+ =
− + − +− −
+ =− + − +
+ =− + − +− −
− =− + − +
+ =− + +
+ =+ + + +
+− =
+ + =++
( )
( )
22
2
22
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
169, 4 17
2
3610, 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
xx
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
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
11 622,
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
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
− + =
− − + + =
+ − + + =
−=
−+ − − + + =
+ + = +
+ − + + =
= +
− − =
− + − + − + 72 72 0x− + =