This document provides 30 equations and inequalities and asks the reader to solve them on the set of real numbers. It uses variables like x, square roots, exponents, and basic arithmetic operations. The problems range from simple one-variable equations to more complex expressions with multiple variables. The goal is to calculate the value(s) of the variable(s) that satisfy each equation or inequality.
Solving Poisson’s Equation Using Preconditioned Nine-Point Group SOR Iterativ...inventionjournals
A well-designed preconditioning of the partial differential equations problems reduces the number of iterations to reach convergence. Dramatic improvements are possible, but the difficulty is to construct the suitable preconditioner.The construction of a specific splitting-type preconditioner in block formulation for a class of group relaxation iterative methods derived from the finite difference approximations have been shown to improve the convergence rates of these methods. This paper is concerned with the application of suitable preconditioning techniques to the Nine-Point Group SOR (N-P SOR) iterative method for solving Poisson’s Equation. Preconditioning strategies which improve the rate of convergence of these iterative methods are investigated. The results reveal the improvements on the convergence rate and the efficiency of the proposed preconditioned Group iterative method.
Ernest f. haeussler, richard s. paul y richard j. wood. matemáticas para admi...Jhonatan Minchán
Ernest f. haeussler, richard s. paul y richard j. wood. matemáticas para administración y economía. (12ª edición). año de edición 2012. editorial pearson
Solving Poisson’s Equation Using Preconditioned Nine-Point Group SOR Iterativ...inventionjournals
A well-designed preconditioning of the partial differential equations problems reduces the number of iterations to reach convergence. Dramatic improvements are possible, but the difficulty is to construct the suitable preconditioner.The construction of a specific splitting-type preconditioner in block formulation for a class of group relaxation iterative methods derived from the finite difference approximations have been shown to improve the convergence rates of these methods. This paper is concerned with the application of suitable preconditioning techniques to the Nine-Point Group SOR (N-P SOR) iterative method for solving Poisson’s Equation. Preconditioning strategies which improve the rate of convergence of these iterative methods are investigated. The results reveal the improvements on the convergence rate and the efficiency of the proposed preconditioned Group iterative method.
Ernest f. haeussler, richard s. paul y richard j. wood. matemáticas para admi...Jhonatan Minchán
Ernest f. haeussler, richard s. paul y richard j. wood. matemáticas para administración y economía. (12ª edición). año de edición 2012. editorial pearson
Nghệ thuật trần thuật trong tiểu thuyết hồ anh tháitruonghocso.com
E2 f1 bộ binh
1. CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 2 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
1
CHUYÊN ĐỀ PHƯƠNG TRÌNH – BẤT PHƯƠNG TRÌNH CHỨA CĂN THỨC
PHƯƠNG PHÁP SỬ DỤNG LƯỢNG LIÊN HỢP – HỆ TẠM THỜI
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Bài 1. Giải các phương trình và bất phương trình sau trên tập hợp số thực
( )
( ) ( )( )
( )
2 2
2 2
2 2
2
22
2
1, 6 2 4
2, 3 8 3 1 7
3, 5 2 1 3 1
4, 4 6 4 5 1
5, 2 4 2 2 2
6, 2 4 1 3 5
7, 2 1 2 1 2
8, 2 1 3 1 0
9, 4 1 2 10 1 3 2
10, 1 1
11, 3 2 2 2 6
12, 2 4 2 5 1
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
+ − + =
+ − + =
− − = +
+ + − + + =
+ + + = −
+ − + = +
+ + − − + =
− + − + =
+ ≥ + − +
+ − − ≥
+ − = + +
− + − = − −
− + 2
2 2
4 6 11
14, 5 3 3 1 1
15, 4 5 1 2 1 9 3
x x x
x x x
x x x x x
− = − +
− + − = −
+ + − − − = +
( )
( )( )
( )
2
2
3
2
2 2
2
2
2 2
16, 1 3 3 4 2
17, 4 3 19 3 2 9
18, 3 1 2 3 4 2 2 1
19, 1 1 1 3 4
20, 2 3 4 3 5 9 6 13
21, 3 1 4 3 2
22, 4 3 10 3 2
23, 3 1 1
24, 2 4 2 5 2 5
25, 3 1 3 1
26, 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
− + − = − −
+ + − = + +
+ + + = + −
+ + + = +
+ + + = + +
+ − + + + + =
− − = −
+ + − = +
− + − + − = −
+ + = + +
+
3
2 3 3 1
27, 1 10 2 5
28, 3 3 1 2 2 2
29, 18 78
30, 3 1 2 1
x x x
x x x x
x x x x
x x
x x x
+ + = + + −
+ + + = + + +
+ + + = + +
= + +
+ = + +
Bài 2. Giải các phương trình và bất phương trình sau trên tập hợp số thực
( )
23
2 2 2
34 3 2
32 24
2 3
2 2 2
2 2 2
2 2
2 2
1, 6 7 1
2, 3 2 4 3 2 5 4
3, 3 4 1 1
4, 77 3 2
5, 2 11 21 3 4 4
6, 1 2 1 3 1
7, 3 2 6 5 2 9 7
8, 3 6 16 2 2 2 4
9, 2 23 4 2 2 7
10, 2 1 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
11, 1 1 1 2 5
12, 2 3 5 2 3 5 3
x
x x x x
x x x x x
+ + + + − =
+ + + − + >
( )
( )
( )
( )
( )
( )
2 2
2
2 2
2
2 2
2
2 2
2 2
2
13, 4 1 1 2 1 2
14, 3 1 6 3 14 8 0
15, 9 1 4 3 2 3
16, 5 12 3 5
17, 2 3 2 6
18, 9 20 2 10 3
19, 3 2 1 3
20, 1 8 4
21, 3 2 3 4
22, 3 2 1 2 3
23, 3 1 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
3 2
24, 2 5 4 2
x
x x x
+ +
+ − ≤ −
2. CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 2 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
2
Bài 3. Giải các phương trình và bất phương trình sau trên tập hợp số thực
( ) ( )( )
2 2 2
2 2 2 2
2
3 2 3 2
22
2 2
1, 4 9 5 2 1 1
2, 8 1 3 5 4 7 2 2
3, 3 19 3 2 7 11 2
4, 3 7 3 2 3 5 1 3 4
5, 2 1 3 2 4 3 5 4
6, 1 1 4 3
7, 2 1 3
8, 9 1 7 3 1 3 4
9, 2 7 10 12 20
10, 5 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
+ + − + − = −
+ + + = + + −
+ + − = + +
− + − − = − − − − +
− + − < − + −
+ + ≤ +
+ + + + − =
+ ≤ + − +
− + = + − +
− 33
2
2
2 2
9 2 3 1
11, 10 1 3 5 9 4 2 2
12, 3 4 5 3 8 19 0
13, 2 2 2
14, 2 11 15 2 3 6
15, 1 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
+ − = + −
+ + − = + + −
+ − − + − − >
− ≤ − − − −
+ + + + − ≥ +
− + − + + =
Bài 4. Giải các phương trình và sau trên tập hợp số thực
( )( )
2 2 2 2
38 84
2 2
3
3
3
2 3
3 3
2 2
1, 2 1 3 2 2 2 3 2
2, 17 2 1 1
3, 2 1 2 1
4, 1 1 1 1 2
5, 2 1 6 3 3
6, 9 11 5 12 1 2
7, 4 3 3 1 2 2 3
8, 2 3 3 13 1
9, 7 7 7 6 5 1
10, 2 5 12 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
− + − + = + + + − +
− − − =
− + + + + =
+ − − + =
+ = + + +
− + = + + + +
− + − = + +
− + = +
+ + = − + −
+ + + + + = +
3 2 4
32 3
2 2
3 2 2 2
5
11, 2 5 5 1 6 2
12, 15 30 4 27 27
13, 2 2 1 14 2
14, 3 4 7
15, 3 8 2 15
16, 1 4 9 16 100
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. CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 2 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
3
Bài 5. Giải các phương trình và bất phương trình sau trên tập hợp số thực
( )
2 2
2 2
3 2
2 2
3
2
3
2
2
3
3 2 3
1, 2 8 8 2
2, 2 8 6 1 2 2
3, 4 1 2 3
4, 9 24 16 59 149 5
5, 2 1 3
6, 1 1 2
7, 2 1 1
8, 4 1 5 14
9, 2 10 12 40
10, 2 1 3 2
11, 3 3
12, 1 2
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
+ − + − =
+ + + − = +
+ = − + −
− + − − + = −
− + + =
+ − − =
− + − <
+ = − +
− + − = − +
+ = + + −
+ + >
− + = −
+ 2 2
3 32 23 3
2 2
5 2 3 1
14, 2 2 2 1 2 1
15, 3 4 2 4 5
16, 5 4 2 1 5 4
x x
x x x x
x x x
x x x x
+ = + +
+ + + = + +
+ − + =
+ − + = −
Bài 6. Giải các phương trình và bất phương trình sau trên tập hợp số thực
3 2
2 2
3 2
2 2
2 2
2 2
2 2
2
1, 1 3 2 4
2, 12 13 4 5 1
3, 2 6 18 1 2 4
4, 3 2 4 4 1
5, 3 5 3 3 2 5
6, 1 6 2 3 1 5 6
7, 3 7 2 5 2
8, 7 6 7 3 2 2 4
9, 5 2 3 3
10, 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 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
3
2 2
3 6
11, 2 2 1 2 8 3 2
12, 2 3 2 5 0
13, 3 4 4 2 1
14, 3 2 1 0
15, 4 5 3 5
16, 2 1 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
− +
+ + − + = + +
− − + + =
− − = − − −
+ − + − =
+ − = +
− − = + −
4. CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 2 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
4
Bài 7. Giải các phương trình và bất phương trình sau trên tập hợp số thực
( )
( )
( )
2 2
2
2
2
2
2 2
4 3
1, 6 5 1 3
7
3
2, 2 6 3 2
1
3, 2 3 1
2 3
3 1
4,
2 1 1 3 3
1 4
5, 5 2 4 2
27
7 83
6, 13
2 1 3 1
1 1
7, 3 1
1 1
9 3 8
8, 3
2 1 3 1
5 15 8
9, 8
2 1 3 1
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
x x
x
x x
+
+ − + =
+ + + + + = +
−
− + =
−
−
=
− − + − −
+
+ + − =
++
+ = +
− − + −
+ ≥ −
− − + −
+ +
+ ≤ +
+ − − −
+ +
+ ≤ +
+ − − −
( )
( )
3 2
2
2
2 2
2
2 2
2 2
2
2
2 2
2
2
3
10, 3 1 1 5
6
9 2 1
11,
2 43
2 1
12, 2 1 3 2
2
4 1 5
13, 2
14, 2 5 12 2 3 2 5
15, 4 3 2 3 1 1
1 2
16,
1
17, 1 2 5 4 1 2 2
5
18, 1
2 1
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 x
x
x
+
− + − + + − = +
−
+ +
+ =
+ + −
−
+ + − =
+ − = + −
+ + + + + = +
− + − − + ≥ −
− +
=
+
− − + − + = +
+ − =
+
−( ) 2 2
2
2
4 2 4 2 2
2
3 4 9
40
20, 16
16
21, 2 1 2 1
22, 4 1 9 1
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
23, 21
3 2 9
3 2 3
24, 3
3 1
7
25, 3 5
2 2
4 20
26, 3
3 3
4
27, . 1 1
2
2
28, 1 3 3 2
4
29, 3 5 1 4 5 3 2
2
30, 2 1 1
2 9
1 1 2
31,
12 8
32, 2 4 2 2
9 16
7 7
33,
34,
x
x
x
x x
x
x
x
x
x
x x
x
x
x x
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
22
2 2
7 2 3
1
1 1
1 5
35, 1
63 3
1
36, 3
2 1
1 2 3
37,
133 4
1 2 6
38, 1
93
1 2 3
39,
8 1 3
5 2
40,
9 3
1 1
41,
31 2 1
4 1 3
42,
xx
x
xx
x x
x
x x
xx
x
xx
x x
x x
x x
x x
x x
x x
xx x x x x x
−
≤ +
+ −
−
< +
−+ −
+ = +
−
+ − −
≥
−+ −
+ −
≤ +
−−
+ − +
>
− + −
+ −
=
− −
− +
<
+ − +
− =
+ + − +
5. CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 2 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
5
Bài 8. Giải các phương trình và bất phương trình sau trên tập hợp số thực
( )
( )
( )
2 2 2
2 2 2 2
2
2 2
2 2 2 2
2 2
1, 2 2
2 2 2 2
2, 1 4 9 0
2
3, 3 4 4
5
4, 2003 2002 2004 2003 2 2005 2004
5, 2 3 4 5 6 7 8 9 10 11 12
6, 3 5 9
7, 7 2 3 5 49
8, 2 3 3 2 1 2 2 1
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 x
+ −
+ =
+ + − +
− + − + + + =
+ + + >
− + + − + = − +
+ + + + + = + + + + +
− − > −
− + − ≤ −
+ − + − − = − + −
( )( )
( )( )
( )( )
2
2 2
2
2
2 2
2 2
, 4 3 1 3 16
10, 3 1 2 3 2 3 2
11, 3 1 2 3 4 2 2 1
12, 5 4 3 5 5 10 20 16 4 12
13, 2 3 1 11 33 3 5
14, 2011 1 1
15, 2 22 2 3
3
16, 2 4
17, 4 1 2 2 1
18, 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
x x x x x
x
+ − − + ≤
+ − − + + =
+ + + = + −
− + + + > − − + + + +
+ + + = − + + −
= + − −
+ + + = + +
− + − = −
− + = − + +
( )( )
( ) ( )
( )( )
2
4 4
2 3 2
2
2 2
23
2
2
8 10 2 8 10 2
19, 3 2 2011 2011
20, 8 3 4 2
21, 3 1 3 2 3 4
2
22, 4 2 2 2 3
23, 1 2 4 1 2 1
24, 6 5 1 2 4
25, 1 2 6 7 7 12
26, 2 6 2 1 3 4
27, 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
+ + − + + =
+ = − +
− ≤ − + −
+ − − − + + − ≥
+ − − ≥ −
+ − ≥ − − +
+ > − + − −
+ + + + + ≤ + +
+ + + − − =
+ + − = − 1
2 2 1
28, 2
2 1
x x x
x
x x
+
+ + +
= +
+ +
6. CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 2 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
6
Bài 9. Giải các phương trình và bất phương trình sau trên tập hợp số thực
2 2
2 3
2 3
2
24
2
4 2 2
3 2
2
2 3
4
1, 3 2 1 5 4 4
2, 7 14 3 4 21 32
3, 2 5 1 6 2
4, 3 1 1
1
5, 15 1
6, 4 28 3 4 12
1
7, 1 5 2
2
5
8, 3 3 2 2 6
2 1
9, 4 2 8
10, 1 2 1 2
11, 9 2 9
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 x x
x
− + − =
− = − +
− + + − = −
+ + = + +
+ + = +
+
− = − − −
−
− − − − =
− + − ≤
−
+ − = −
+ + − = + −
− − = −
( )
( )( )
( ) ( )
( )( )
2
2
2
2
2
2
2 2
2 2
3
2 2
1 1
9 12 4
3 31
3 4 9
13, 2 3
3 3
14, 4 2 2 6 1
15, 3 3 3 4 1
16, 3 2 7 2 9 1 11
3 18
17,
11 1
3
18, 1 4
2
19, 3 6 2
20, 3 1 1 3
21, 1
2 1 4 1
22, 2 6 8 2
x x
xx
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
− + − = −
−−
−
≤ +
−
+ − + − <
+ = + −
+ − + + = − +
+ +
<
++ − +
− + + ≥ +
+ − + = −
+ + − − = −
> −
+ − +
+ − +
2 3 2 2
2
2
2 2 2
4 6 3 4 3 3 1
23, 6 6 3 4 2 5
24, 2 4 3 2 3 4
25, 2 2 3 4
11 14
26, 1
2 7
x x x
x x x x x x x
x x x x
x x x
x x x
+ − − + − + >
− + + + + ≤ − + + + +
− + + = + +
− − + + =
+ =
+
7. CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 2 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
7
Bài 10. Giải các phương trình và bất phương trình sau trên tập hợp số thực
( )
( )
2
2
2
2
2
3 2
3
2
2 2
2 2
2
3
23
1, 2 1 5 1 1
2, 2 5 6 2 8 9 4
3, 4 2 22 3 8
9 8 32
4, 2 4
16
5, 3 1 8 3
6, 3 92 4 108 28
7, 1 2 2 2
8, 3 2 4 3 4
9, 2 92 2 1 1
5 4
10, 2 5 24 23
3
11, 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
− + − = +
+ + + + + =
+ + − = +
+ −
− ≤
− + = −
− + − = −
+ + − = + −
− = − + − −
+ + ≥ + + + −
+
− + + − =
− + ( )
( ) ( )
( )
( )( )
( )
3 3
3
2
2
2
2
2
2 2
2 1
5 1
12, 1 5 2
4 2
13, 4 1 9 1 2 1
14, 13 1 9 1 6
7
15, 1 1
4
16, 1 2 1 2 3
17, 1 1
18, 2 1 3 2 6
19, 5 3 2 3 23
20, 3 1 2 1
21, 1 3 4 1
22, 2 3 2 3 2
23
x x
x x x
x x x x
x x x
x x x
x x 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 1 2 2 11 2
24, 2 9 2 8
25, 2 4 3 2 3 3 7 6 5 7
26, 5 1 2 2 10 3 13
27, 5 6 3 21 19 42
28, 3 11 3 2 7
29, 4 6 2 13 17
x x x x x
x x x x
x x x x x x
x x x
x x x x x x
x x x
x x x x
+ + − + + − ≤ −
+ − = − −
− − + + − + − = −
+ + = − +
− + + − + + = + −
+ + = +
− + − = − +
8. CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 2 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
8
Bài 11. Giải các phương trình và bất phương trình sau trên tập hợp số thực
( )
( )( )
( )
( )
2
2
2
2
2
2
4 3
1, 3 5 2
6 1
6
2, 2 1 1
2 1 1
3, 2 9 8 6 1 3 4 5
2
4, 4 3 2 1
2 3
1
5, 3 2
6
6, 9 5 1 2 1
3 1 2
7,
3 13 3 16
3 2 9
8,
3 1 3
9, 17 9 1
2 2 1
12
10, 6 1 2 4
2 1 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
xx x
x
x x
x x
x
x x
x x
+
+ − − =
−
≥ + + −
+ +
− − − + + + =
+
+ − − =
−
+
+ = +
+ − = +
+ − +
<
+ + +
− −
>
+ + +
≤ + − +
+ − +
+
≥ + + −
− + +
( )
2
2
2
12, 3 4 5
2 5 1
1 4 3
13, 1
4 3 3 4 3 1
2 9
14, 2 3
1 3 2 2
1 3 1 1
15,
2 1 2 1
2 1
16, 3 1 2
3 2 1
3 3 2 3 2
17, 3
2 1 2 3
4 12 4 2 3 1
18,
3 10 3 1 3
1
19, 1
1 1
2
20,
x
x
x x
x
x x
x x x
x x
x x x
x x
x x x
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 3
2
21, 3 2 2
2 5
x
x x x
x x
x x x
x
≤ +
+ − −
− +
+ + − ≤
+
9. CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 2 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
9
Bài 12. Giải các phương trình và bất 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
2
2
4
1, 1 2 3 2
2 3 2
3 14 4
2, 3 4 1
2 4 1 2
3, 4 4 1 4 4 2 3 2 5 2 4
3
4, 2 3 5
3
1
5, 1 1
1
3 1
6, 3 2
2 4 2
5 5 2 1 1
7,
1 3 1
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 x x
x x x
x x x x
= + − +
+ + − − +
+ +
= + + − −
+ + − +
+ − ≤ + + + + + + +
+
= + + −
+ + −
−
= + + − −
+
+ −
≤ − +
+ + −
+ + − +
=
+ + + −
( )
( )
( )
2
2
2
2 2
2
3 6 2 2
, 4
2
1 10
9,
303 2 4 2 9 15
3 5 1
10,
2 5 4 5
5 26 2 5
11,
2 2 2 1 3 2
3 1
12,
1 2 1 3 3
13, 5 6 3 21 19 42
2 1 1 1
14,
9 1
3
15, 2 1 2
3
7 13 8
2
3
16, 5 5 2
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
+ + + +
≤
− −
>
+ + − + + +
+ −
=
+ +
+− −
≤
− + − −
−
=
− − − − +
− + + − + + = + −
+ − +
≥
−
+ − >
+ − +
+ + >
( )
2
2
2
2
2
30
17, 5 3 5 5 2 3 1
10 5
4 1
18, 4 1 2
3 4 2 1
2 3 2 1 1 9 4
19, 4.
1 4 1
x x
x x
x
x
x x x
x x x
x x
x x
+ +
−
= − − + +
−
−
= + + − +
+ + + −
− − − −
≤
− −