e1 f4 bộ binh
DESCRIPTION
Một số bài toán về phương trình bậc cao, tiền tuyến trong công tác giải phương trình vô tỷ trong trường hợp bất khả kháng.TRANSCRIPT
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− + =