1.
CHUYÊN ĐỀ PHƯƠNG TRÌNH – BẤT PHƯƠNG TRÌNH CHỨA CĂN THỨC
PHƯƠNG PHÁP SỬ DỤNG ẨN PHỤ
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Bài 1. Giải các phương trình và bất phương trình sau trên tập hợp số thực
1, x − 3 + x = 9
29, 3 3 x 2 + x − 3x 2 − x = 2
2, 3 − x + x 2 − 2 x + x − x 2 = 1
30, 4 x 2 + x + 1 = 6 ( 4 x 2 + x ) + 1
3, x + 2 x + 5 < 4 2 x ( 2 + x ) + 3
2
31, x 2 − 4 x = −2 + x 2 + 5 − 4 x
4, x ( x − 4 ) 4 x − x + ( 2 − x ) < 2
2 2
32, ( 3 − x ) + 3x − 22 = x 2 − 3x + 7
2
5, ( x + 1) + ( x + 1) + 3x x + 1 > 0
2 3
33, x ( x + 5 ) > 2 3 x 2 + 5 x + 2 − 2
6, x 3 + x 2 − 1 + x 3 + x 2 + 2 = 3
34, 12 − 4 ( 4 − x )( x + 2 ) ≤ x 2 − 2 x
7, 2 x 2 + 5 x + 2 − 2 2 x 2 + 5 x − 6 = 1
35, x 2 + 7 x + 4 = ( 4 x + 8 ) x
8, 3 x + 21x + 18 + 2 x + 7 x + 7 = 2
2 2
36, x 2 − 7 x + 6 + x 2 − 7 x + 3 = 3
9, 3 x 2 + 6 x + 4 < 2 − 2 x − x 2
37, x 2 + x + 7 + x 2 + x + 2 = 3 x 2 + 3x + 19
10, 4 x − 12 x − 5 4 x − 12 x + 11 + 15 = 0
2 2
38, 2 x 2 + x + 7 − 2 ( 2 x 2 + x + 1) = 3x 2 + ( x + 1)
2
11, x ( 2 x + 3) > 3 − 4 x − 6 x
2
39, 7 (1 + x )( 2 − x ) > 1 + 2 x − 2 x 2
12, 4 + ( x + 1)( 2 + x ) ≤ x 2 + 3 x
3
13, x 2 − 34 x + 48 ≥ 6 ( x − 2 )( x − 32 ) 40, x 2 + 3 − 2 x 2 − 3 x + 2 = x + 6
2
14, 9 x 2 + 3x + 12 = x ( x + 3) − 2 11 28
41, x 2 − 3 x − 5 9 x 2 + x − 2 = − x
4 9
15, 3 x 2 − 2 x + 15 = 7 − 3 x 2 − 2 x + 8
42, 4 x x + 1 + x + x = 5
3 2
16, 3 x + 5 x + 8 − 3 x + 5 x + 1 > 3
2 2
43, x x 2 + 4 + 5 ( x 2 + 2 ) = 20
2
17, 3 x 2 + 2 x = 2 x 2 + x + 1 − x
44, x 1 + x = 2 x 3 + 2 x − 1
18, 2 x + x 2 = 2 ( x 2 + 2 x + 4 ) + 3
1 x
45, 1 + + 2 =3
19, x + x + 2 = x ( x + 2 ) − 2
2 x x +1
x +1 x −1
20, 18 x 2 − 18 x + 5 = 3 3 9 x 2 − 9 x + 2 46, + =2
x −1 x +1
21, 3 3 x 3 − 3x + 2 = 2 x 2 − 6 x + 5
3+ x x +8
(
22, 3 x − 2 x + 9 = 3 2 − 3x − 2 x + 1
2 2
) 47,
x
+
x
=5
4x +1 1
23, 2 x ( x − 1) − x > x 2 − x + 1 48, + =5
4x x
24, 3 x 2 + 15 x + 2 x 2 + 5 x + 1 = 2
49, x2 − 4 x + 3 = 4x − x2
25, ( x + 5 )( 2 − x ) = 3 x 2 + 3 x
50, 8 + x − 3 + 5 − x − 3 = 5
26, 5 x + 10 x + 1 > 7 − 2 x − x
2 2
51, 1 − x − x + 2 − x − x = 1
27, 2 x + x − 5 x − 6 = 10 x + 15
2 2
1
52, 5 + x + 2 3 − x > 3− x − 2
28, ( x + 1)( x + 4 ) ≤ 5 x + 2 x + 28
2
3
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
1

2.
Bài 2. Giải các phương trình và bất phương trình sau trên tập hợp số thực
1, 4 x + 3 + 2 x + 1 = 6 x + 8 x 2 + 10 x + 3 − 16
1
2, 2 x + 1 + 9 − 2 x + 3 9 + 16 x − 4 x 2 > 13 25, x 2 + 2 x x − = 3x + 1
x
12 − x x − 2 82
3, (12 − x ) + ( x − 2) < 26, x 2 + 3 x 4 − x 2 = 1 + 2 x
x−2 12 − x 3
1 3x 27, 1 − x 2 + 2 3 1 − x 2 = 3
4, > −1 3
1− x 2
1 − x2 28, 1 + x − x2 = x + 1 − x
2
7 5x
5, ≤ +2 29, x + 7 + x + 2 x 2 + 7 x = 35 − 2 x
2− x 2
2 − x2
30, 2 x + 3 + 1 + x = 3 x + 2 2 x 2 + 5 x + 3 − 2
( ) + 32
2
1
6, x + 16 + x = x + 16 + x 22
2 5 1
31, 5 x + > 2x + +4
1− x 8 2 + x 2 x 2x
7, 8 + =2
2+ x 1− x 32, x −1 + x + 3 + 2 ( x − 1)( x + 3) + 2 x = 4
8, 3 2 + x − 6 2 − x + 4 4 − x 2 = 10 − 3 x 33, 3 x − 2 + x − 1 = 4 x − 9 + 2 3x 2 − 5 x + 2
x
9, x + =2 2 34, 1 + x + 8 − x = 3 + (1 + x )( 8 − x )
x −1
2
2x 3 1 1
35, 3 + x + 6 − x = 3 + ( 3 + x )( 6 − x )
10, 3 + + =2
x +1 2 2x 36, 3 x + 1 + 2 − x + 2 2 + 5 x − 3 x 2 = 9 − 2 x
11, x + 4 + x − 4 = 2 x + 2 x 2 − 16 37, x + 2 − x 2 + x 2 − x 2 = 3
12, 4
x −1 + 4 x = 4 x + 1 38, x + 4 − x = 5 + 4 x − x2
x 35
13, x + > 39, x+ 2 + 6− x = 8− ( x + 2 )( 6 − x )
x −1 2 12
(2 − x) + 3 ( 7 + x ) = 3 + 3 ( 7 + x )( 2 − x )
3 2 2
40,
14, x + 1 − 12 − x = − x 2 + 11x − 23
8− x
15, 7 + x − 9 − x = − x 2 + 2 x + 63 41, 1 + x + 8 − x − (1 + x ) =3
1+ x
16, 3 − x + x − 1 − 4 4 x − x 2 − 3 + 2 ≥ 0
42, 2 1 − 4 x + 5 x + 1 = (1 − 4 x )(1 + x ) + 5
17, 4
x − x −1 + x + x −1 = 2
2 2
x 2 − 6 x + 15
43, x 2 − 6 x + 18 =
18, 9 ( x + 1) − x 2 = x + 9 − x x 2 − 6 x + 11
20 + x 20 − x x −1
19, − = 6 44, 1 − x + ( x − 1)( x − 2 ) + ( x − 2 ) =3
x x x−2
x−2 + x+2 x+2
20, x2 − 4 − x + 1 = 45, x 2 − 4 + 4 ( x − 2 ) = −3
2 x−2
8x2
21, x + 17 − x 2 + x 17 − x 2 = 9 46, 1 + 2 x − 1 − 2 x =
1 + 1 − 4 x2
22, x + 4 − x 2 = 2 + 3x 4 − x 2
2(2 − x)
2
1 1 47, x − 4− x =
23, 1 − −2 +1 > 3 2 + 4 x − x2
x +1 x
4
24, x + = x −
2
+4
48, ( )(
x + 3 − x −1 1 + x2 + 2 x − 3 = 4 )
x x
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
2

3.
Bài 3. Giải các phương trình và bất phương trình sau trên tập hợp số thực
x +1
1, ( x − 3)( x + 1) + 4 ( x − 3) = −3
x−3
2, 2 1 − x − 1 + x + 3 1 − x 2 = 3 − x
x+3
3, 2 x 2 − 9 = ( x + 5 )
x −3
x −1
4, 2 x 2 − 1 = x 2 + 2 x + 5
x +1
2
5, = 1 + 3 + 2x − x2
x +1 + 3 − x
6, x 2 − x = ( 2 − 2 x ) x + 3
7, x 2 − 3 x + 6 = 2 ( 2 − x ) 3 + x
8, 2 x 2 − 7 x + 15 = ( 9 − 4 x ) 3 + x
9, x 2 − 1 = 2 x x 2 + 2 x
10, x 2 + 4 x = ( x + 2 ) x 2 − 2 x + 4
11, x + 1 = x2 + 4 x + 5
12, 3 x = 3x 2 − 14 x + 14
13, 7 x + 7 + 7 x − 6 + 2 49 x 2 + 7 x − 42 < 181 − 14 x
14, ( 3 + x ) ( 4 − x )(12 + x ) + x = 28
2 x 2 − 3x + 5
15, = x2 + 2x −1
5 − 2x
( )
16, 2 x 2 + 14 − 2 x 2 + 8 x x + 8 x − 14 x ( x + 8 ) + 24 = 0
17, x 2 − x − 2 1 + 16 x = 2
( )(
18, x + 15 x + 36 x + 5 x + 4 = 520 x )
x+4
19, 2 x 2 − 16 = ( 6 + x )
x−4
 1 1 2 3
20,  x −  x 2 + 3x + = x
 3 9 9
21, x 4 − 2 x 2 + x = 2 ( x 2 − x )
22, 5 x 2 − 11x + 7 + ( 4 x − 5 ) x 2 − x + 1 = 0
5x2 − 9 x + 7
23, = x2 + x + 1
5 − 4x
24, 5 x 2 − 11x + 7 = 2 ( 3 − 2 x ) x 2 + x + 2
1
25,5 16 − x 2 − =4
16 − x 2
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
3

4.
Bài 4. Giải các phương trình và bất phương trình sau trên tập hợp số thực
x2 + 2
1, ( x + 1) − 3x
2
<1
x
2, ( x + 2 ) = 5 x 3 − 4 x + 8
2
3, x 2 + 5 x − 1 ≤ 6 x 3 − x
4, 7 x ( x 2 + 3) + 6 ≥ ( x + 3)
2
2 ( 2 x 2 + x + 1)
5, ≤ 2 x3 + x
5
6, 2 x 2 + 3 x + 4 − 5 x 3 + 2 x = 0
3 ( 4 x 2 + x + 1) 4x2 + 1
7, <
10 x x
3 ( x + 1)
2
x2 + x + 1
8, =
10 x x
x2 + 1
9, 3 ( x + x + 3) = 10 ( 2 + x )
2
x+2
10 x x − 1
10, 3 ( x 2 − x + 1) ≤
x
11, ( x − 1) + x − x = 0
2 3 4 2
2
12, x 2 + 2 + x 3 x + = 2x
x
13, ( x − 1) + 3 x 2 ( x 2 − 2 ) = 3
2
x2 − 2
14, 3x 2 + 4 x − 6 > 7 x
x
x −1
15, x 2 + ( x + 1) ≤3
x +1
x2 − 3
16, 2 x 2 − 5 x − 3 x ≥6
x
17, 6 x 2 − 3 3 x 2 − 2 x − 1 ≤ 4 x + 4
18, 2 ( 2 x 2 + 8 x + 6 ) = 4 + x
( )
3
19, x −1 + 1 + 2 x −1 = 2 − x
x +1
20, 2 x 2 − 8 x + 3 ( 5 − x ) = 12
x −5
21, 2 x 2 − 3 x + 1 ≥ 4 x − 4 x 2 − 3 x + 1
x 4 − 4 x 2 + 16 4 − x2 x
22, ≤ + +1
x (4 − x )
2 2
x 4 − x2
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
4

5.
Bài 5. Giải các phương trình và bất phương trình sau trên tập hợp số thực
x +1
1, 3 x + 5 < ( 3 x + 6 )
x+2
2, 3 ( x 2 − 3x + 9 ) < 2 x − 3 x − 6
3, 3 ( x 2 + 5 x + 9 ) ≤ 2 ( x + 3) + 5 x
x− x
4, ≥1
1 − 2 ( x − x + 1) 2
x −2 1
5, ≥
6 ( x2 − 2 x + 4) − 2 x 2
3x − 4 x
6, ≤1
5 ( x 2 + 13 x + 16 ) − 12
7, 3 x 2 + 12 x + 3 − x ≤ 1 − x
x +1
8, ≤1
2 x + 5x + 1 + 3 x
2
9,
( x +1 )( x +3 ) >3
x 2 − 10 x + 9
10, 7 ( x − 1)( x − 4 ) ≤ x − x − 2
11, x 2 − 6 x + 1 ≥ (1 + x ) x
12, 4 + x 2 = 5 x ( x − 2 )
2 x+2
13, ≤
3 x ( x + 1)( x + 4 )
7 x 1
14, ≥
4 x + 10 x + 1 x + 2
2
2 9 x2 − 5x + 1
15, . ≥ x
5 3x − 1
4x2 − 2x + 1
16, ≤ x
2x +1
17, 6 ( x 2 − 6 x + 4 ) + x ≤ 2 ( 2 + x )
18, x 2 + 15 x + 9 ≤ 6 x ( 3 + x )
x3 − 7 x 2 − 8
19, ≥ 2x
3 x −7
20, ( x − 2 ) ≤ ( x 2 + 4 ) x
3
21, 2 + ( x − 2) ( 4 + x2 ) ≤ x + 2 x
22, x 3 + 5 x 2 + ( x 2 − 10 x + 1) x ≤ 1 + 5 x 2
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
5

6.
Bài 6. Giải các phương trình và bất phương trình sau trên tập hợp số thực
1, 6 x 2 − 7 x + 13 ≤ ( 7 − 6 x ) x 2 + 3
2, 15 x 2 − 7 x + 13 + (12 x − 7 ) x 2 + 3 = 0
18 x 2 − 7 x + 19
3, > 5 + 2 x2
7 − 12 x
18 x 2 + 15 x − 6
4, = 3x + 1 − 2
5 − 12 x
5, 8 x 2 − 9 x + 8 + ( 8 x − 5 ) 1 + 3 x = 0
6, ( x + 1) + 2 ( 3 − x ) 2 x + 1 = 6 x − 5
2
2 x2 − 5x + 4 2 ( x + 1)
7, −1 =
2x − 3 2x + 3 +1
8, 2 + x ( 3 x − 5 ) + ( 3 x − 5 ) x 2 − 1 = 0
9, 4 (1 + x ) = ( 2 x + 1) 2 x + 1
10, x + 4 + x 2 − x + 4 = 3 x 2
11, 7 x 2 − 2 x = 1 + 2 x 2 − x + 1
12, 7 x ( 2 x − 1) ≤ 2 x ( 2 x + 1)
3 2
13, x + 4 x2 + x − 7 = x + 7
4
14, 3x 2 − 28 + 8 x 2 + x − 7 = 0
15, 23 x 2 − 32 x = 4 x 3x 2 + 5 x + 2 + 7
16, 2 x 2 + x − 4 = 2 2 x 2 + 3 x + 4
2 x − 1 − 28 x 2
17, 3 x 2 + 1 <
24 x − 1
x 2
2 − x − 6 x2
18, =
1 + 1 + 5x2 5 ( 2 x − 1)
5 13
19, 3x 2 + x + + 2 x 2 x 2 + x + 5 = 0
2 4
2 x2 − 5x + 7 + 2 x2 + 2 x − 3
20, ≤ 9 − 2x
x2 + 2x − 3
x 2 + x + 10 3 ( 2 − x )
21, ≥ −1
4 x 2 − 5 x + 26 5 − 2x
5 x + 17
22, > x+5 − x
16 x + 1
2 − x 2 (1 + x )( x − 4 )
23, ≤
11 − 2 x x − 3x + 4
x +3
2
24,
4− x
(
= 4 x + 1 −1 )
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
6

7.
Bài 7. Giải các phương trình và bất phương trình sau trên tập hợp số thực
1, 2 ( 2 − x ) + 7 x 3 − 4 x ≤ 16
2
2, 4 x 4 − 8 x 2 + 7 2 x 4 − x 2 > 2
3, 2 x 2 + 7 x + 1 + x + 1 ≤ 3 x
3 x2 + 6x + 1 + x
4, ≥1
5 x −1
4 x2 + x + 1 − 3 x + 3
5, ≤ −1
x−2
3 x2 − 5x + 4 − 5 x + 3
6, ≤1
1− x
4 x + 7 x − 16
7, ≥6
( x + 1)( x + 4 ) + x − 2
( x + 1) + 3 ≤ 2 + x
2
8,
x2 + 3x + 4 + x
15 + ( 2 x − 1)
2
9,
x 2 + 3x + 4 − 2 x
≥4 ( x +1 )( x +2 )
2 (1 + x )
2
(
10, 2 x + 1 )( x +2 ≤ ) x2 + 3x + 1 − x
2 4 x 2 − 3x + 1 − 5 x − 4
11, ≤1
2x − 3
7 4 x 2 − 5 x + 1 − x + 15
12, =2
7−x
13, 6 x 2 + 24 x + 26 ≤ x (1 − x )
14, 6 x 2 + 24 x + 26 = ( 7 − x ) x
 4 
15, ( 3 − x ) ≥ 6 +  3 x − + 8  2 x − 1
2
 x 
 4
16, ( x − 6 ) < 16 + 3x −  4 x − 1 + 33
2
 x
 36 
17, 11x 2 + 19 x −  4 x 2 − 9 = 27 x
 x 
3 1
18, 2 x 2 − 9 x + 3 = 10 ( 3 x − 1)−
x x2
 1 1 3
19,  2 −  2 x − 1 ≤ ( x − 3) +
2
 x 5 2
1 
20, 14 x 2 < 3 + 10  − 4 x  1 − 4 x 2
x 
x 2 − 3 x − 6 10 x 2 − x − 2
21, <
2 + x − x2 x
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
7

8.
Bài 8. Giải các phương trình và bất phương trình sau trên tập hợp số thực
1, x 3 + 12 x ≤ 18 x 2 + 9 ( 3 x − 2 ) 3 x − 2
2, x ( x − 3) + 21x + 9 ( 5 − x ) x − 5 = 0
2
3, 7 x 2 − 6 ≥
9
x
(1 − x 2 ) 1 − x 2
4, x ( 6 − 25 x 2 ) + 9 ( 9 − 4 x 2 ) 9 − 4 x 2 = 0
1 − x 2x −1
5, ≤ 1− 2x
2 x −1
x ( x − 1)( 2 − x )
6, ≥ 2 2 − 3x
3x − 2
 8 
7, x 2 +  x − + 36  2 x − 9 + 4 x ≤ 18
 x 
8, x 3 + ( x 2 − 16 x + 12 ) 4 x − 3 + 8 x 2 = 6 x
x −1
9, ( x + 1) + .( x − 2) ≥ 3
2 2
x
x 2 + x + 1 3 x + 2 ( x + 1)
2
10, ≥ 2
x 3 x + 4 ( x + 1)
x ( 3x2 + 2 x − 4)
11, = ( x − 1)( x + 2 )
3x 2 + 4 x − 8
12, ( 3x 2 + 12 x + 8 ) (1 + x )( 2 + x ) ≤ x ( 3x 2 + 6 x + 4 )
13, 7 x 2 + 5 2 x + 7 = x 4 + 1
14, 4 x 3 + 3 x 2 + 4 x + 1 = 2 ( 3 x + 1) 3 x + 1
7  1 
15, x 2 + 19 x + 11 ≤ +  5 x + + 18  2 x − 1
x  x 
16, x 3 + 13 x 2 − 53x + 39 ≤ ( 5 x 2 − 4 x − 15 ) 2 x − 5
 1
17,  8 x − 2 +  1 − 2 x ≥ 4 x 2 − 10 x + 5
 x
18, ( x − 3) + ( 2 x − 7 ) x − 3 = 0
2
19, 2 x + 1 + 3 x − 2 = 2 x 2 − x − 2 + 3 1 + x
20, 5 x + 10 x − 2 = 2 + 4 x 2 − 4 + 5 2 + x
21, 12 x − 1 + 13x < 2 + 12 x 2 − 1 + 8 x + 1
22, 10 x − 4 + 8 x 2 − 1 = 5 1 + x + 10 x − 1
12 6 
23, 2 x + = 5 +  − 2  x2 + x + 7
x x 
x 4 + 2 x3 − x 2 − 2 x + 3
24, = x2 + x + 1
2x + 2x − 3
2
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
8

9.
Bài 9. Giải các phương trình và bất phương trình sau trên tập hợp số thực
1, x + 7 + 2 ( 3 x − 2 )( 3 − 2 x ) = 5 3x − 2 + 5 3 − 2 x
2, 11 − 3 x + 10 1 − x = 5 x + 1 + 4 1 − x 2
3,
( x − 2 )( x − 7 ) = 2 − 2x
5 − 2x 3 − 2x −1
( )
4, ( x 2 + 5 x + 12 ) 1 − 1 − 2 x = 4 x 2 + 10 x
2 ( x + 3)( 2 x + 3)
5, 2 − 1 − 2 x ≤
x2 + 8x + 2
x 2 − x + 28 9 − 2x
6, =
3x 1 + 3x − 1
x − 7 x + 55
2
3
7, ≥
( 9 − 2 x )( 5 − x ) 4 − 1 + 3x
8, 5 x + 17 + 14 x + 1 = 6 x 2 + 4 x + 3 + 7 3 − x
x3 + 3x 2 − 4 x + 6
9, = 1+ x
6 − x − 3x 2
10, x 3 + 3 x 2 − x + 6 ≤ ( 3 x 2 + x − 5 ) 2 + x
11, ( 3 x 2 + 2 x − 7 ) 1 + 2 x + x 3 + 6 x 2 − 5 x + 12 > 0
10
12, x 2 + x ≤ ( x − 1) x − 1 + 1
x
x3 + 3x 2 − 3x
13, 10 3x − 1 ≥
3x − 1
x + 25 x − 68 x + 12
3 2
5 ( x − 2)
14, =
5 x + 20 x − 4
2
5x −1 + 3
x 3 + 44 x 2 − 33 x
15, ≤ ( x 2 + 4 x − 3) 4 x − 3
6
2 x 3 + 22 x − 11x 1
16, >6 x−
2x + 2x −1
2
2
x + 5 x − 28 x + 12
3 2
17, 6 ( x − 3) ≤
x2 + x − 2
(
x − 2 +1 )
x 3 + 10 x 2 − 23 x + 2
18, 1 + =6 x−2
x2 + x − 2
19, (13 − 4 x ) 2 x − 3 + ( 4 x − 3) 5 − 2 x = 2 + 8 16 x − 4 x 2 − 15
(
20, (13 + 4 x ) x − 1 + ( 4 x + 9 ) x + 1 ≤ 6 2 x + 1 + 2 x 2 − 1 )
21, ( 2 x − 1) x + 1 + ( 2 x + 1) x − 1 = 1
22, ( 4 x − 1) 2 x − 1 + ( 4 x + 1) 2 x + 1 = 4
23, (13x + 1) 1 + x = 2 ( 7 x + 3) x + 1
24, 8 x = 19 + x 3 + 6 x x + 1
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
9

10.
Bài 10. Giải các phương trình và bất phương trình sau trên tập hợp số thực
1, 8 x 3 + 8 = ( 2 x + 3 − 12 x 2 ) 2 x + 3 + 12 x 2 + 18 x
2, ( 3x 2 + 9 x + 5 ) 3 x + 2 + x 3 + 12 x 2 + 18 x = 1
3, x 3 + 12 x 2 + ( 6 x 2 + 8 x − 24 ) x − 3 = 1 + 36 x
4, 9 ( x 2 + 3 x + 6 ) x + 2 = 27 ( x + 1) + x 3
2
x 3 + 12 x 2 + 24 x + 27
5, 2 2 + x ≥
3x 2 + 4 x + 8
8 x 3 + 6 x ( x + 5 ) + 27
6, 5 x + 5 <
12 x 2 + x + 5
7, x 3 + 3 x 2 + 3 x = ( 3 x + 4 ) x + 7
8, x 3 + 6 x 2 + 12 x + ( 4 x + 2 ) x = 20
9, 7 x 3 + 3 x 2 + (12 x 2 + x ) x = 1 + 3 x
3 9
10, 3x x − 5 x + + x2 =
x x
 3  26
11, x 2 + 15 ( x + 1) + 2 x  3x + 10 +  ≤
 x x
3 3x
12, +1 <
3− x 2
3 − x2
9 − 4x 3 − 2x
13, + ≥2
2 − x2 2 − x2
5x 2 + 3x + 1
14, ≥5
( x + 1) ( x3 − 1)
6 x2 − 8
15, +1 ≥
x 4 − x (6 − x)
4 5x
16, > +9
2 − x3 x3 − 2
3
2 − x3 12 x
17, + 14 ≤
1− x 3 3
1 − x3
1 
18, x 2 + 12 x + 16  − 1 1 − x ≤ 12
x 
19, 16 x 3 < (11x 2 − x + 2 ) ( x − 1)( 2 + x )
11 1 + x 2 16
20, ≤
( x + 1)
3
24
x2 + x +1
11
21, (12 x 2 − 25 x + 12 ) 1 + x + 16 (1 − x ) = 0
3
6 x3 − 5 x
22, ≤ 2 x2 −1
3x 2 − 1
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
10

11.
Bài 11. Giải các phương trình và bất phương trình sau trên tập hợp số thực
1, x 2 + 4 x + 9 > 7 x ( x − 3)
x 2 − x + 23
2, > 7 x −7
x−2
(
3, x 2 + 7 x + 6 ≤ 8 x − 1 ( x − 2 ) )
(
4, ( 3 + x )( 4 + x ) ≤ 4 2 x − 1 ( x − 2 ) )
x2 + 8x
5, ≥ 9 x +1
x −1
1  1
6, x + 14 + = 10 1 −  x
x  x
7, ( 4 + x ) + 10 ( 4 − x ) x ≥ 0
2
(
8, x 2 + 11x < 3 3 x + 1 ( x − 3) )
2 x 2 + 3x + 2 + x − 2
9, ≤1
2 x −3
2x2 + 7 x + 8 + 2
10, >1
2 x−x
2 x 2 + 10 x + 8
11, ≤1
x−3 x + 2
12, x + 3 ≤ 3 x + 2 ( x 2 + 7 x − 9 )
13, x 2 + 3x + 2 + x 2 + 3x ≥ 4
2
14, x 2 + 12 x + 2 ≥ 7 x x +
x
x2 −1
15, x 2 + 15 x − 8 x ≥1
x
1 − 2 x2
16, 1 − 3 x ≤ 2 x 2 + 10 x
x
3 − 4 x2
17, 3 > 5 x + 14 x + 4 x 2
x
18, ( 3 x 2 − 3x − 1) 3x −
1
+ 2x ≤ 0
x
1 2x
19, 4 x − ≥
x 3x + 1 − 4 x2
20, x + 3 ≥ 6 x − 4 x 2 − 29 x + 36
21, ( x 2 + 2 − 8 x ) x +
2
+ 12 x ≤ x 2 + 2
x
x2 + 9x + 4 4
22, 2 x+ ≥2
3 x + 2 x + 12 x
CREATED BY HOÀNG MINH THI TRUNG ĐOÀN 3 – SƯ ĐOÀN 1 – QUÂN ĐOÀN BỘ BINH
11