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PHƯƠNG TRÌNH, BẤT PHƯƠNG TRÌNH VÀ HỆ PHƯƠNG TRÌNH
1. ( x + 1) x 2 − 2 x + 3 = x 2 + 1
3. sin 2 n x +
4.
sin
1+ 3 x
1
2 m +1
= cos 2 n x +
x
1
− x 1 − x2 = 1 − 2 x2
2
2.
1
cos 2 m+1 x
với m , n là các số nguyên dương
5. x 3 − 3x = x + 2
−1= 0
oc
.c
om
4x + 2 + x
6. x 4 + 2006 x3 + 1006009 x 2 + x − 2 x + 2007 + 1004 = 0
x 2 ( y + z )2 = ( 3x 2 + x + 1) y 2 z 2
6 x 2 = y (1 + 9 x 2 )
2
8. 6 y 2 = z (1 + 9 y 2 )
7. y 2 ( z + x ) = ( 4 y 2 + y + 1) z 2 x 2
2
2
2
2
2
2 2
6 z = x (1 + 9 z )
z ( x + y ) = ( 5 z + z + 1) x y
4
cos 2x
3
3
+ 4 tan 6 x = 7
9. 6 x + 1 = 8 x − 4 x − 1
10. 3 1 +
2
cos x
11. ( x − x 2 )( x 2 + 3 x + 2007 ) − 2005 x 4 − 4 x = 30 4 x 2 + x − 1 + 2006
6 x 2 x3 − 6 x + 5 = ( x 2 + 2 x − 6 )( x 3 + 4 )
13.
2
2
x + ≥ 1 + 2
x
x
14. x3 − 3x + 3 = 0
15. 2005 − x
4
bo
cu
1
2
x
+
xy
y
+
2z
=
(
)
(
)
8
−3
2
2
12. x + y + 3 xy + 4 xz + 2 yz =
4
x + y + z = 0
x < 0 < y , z
2006
+ 2006 − x
17.
x + y − z = 7
18. x 2 + y 2 − z 2 = 37
x3 + y 3 − z 3 = 1
3
3 y − 1 + x = 3
19.
2
3
x + y = 82
kh
on
g
16. (16cos 4 x + 3) = 2048cos x − 768
3
2005
=1
2 x + 1 + 1 = x3 + 3x 2 + 2 x
20. 16 x 6 − 16 x5 − 20 x 4 + 20 x3 + 5 x 2 + 2 x − 7 = 0
21. 11x 2 − 14 x + 9 + 11x 2 − 2 x + 3 + 17 x 2 + 2 x + 3 = 2 ( 2 x + 4 )
45
22. x 2 + 2 x + 5 − x 2 − 4 x + 40 = x 2 + 5 x +
4
2
3
24. x 2 − 2 x − 3 = x + 3
23. 2 x − 11x + 21 − 3 4 x − 4 = 0
x (4 − y2 ) = 8 y
25. y ( 4 − z 2 ) = 8 z
26.
2
z ( 4 − x ) = 8 x
27. 2 x + 1 + x x 2 + 2 + ( x + 1) x 2 + 2 x + 3 < 0
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x 2 + y 2 + 4 xy = 6
2
2 x + 8 = 3 y + 7 x
1
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− x2 + 6 x − 5
y +1
x = 1 +
x
z +1
31. y = 1 +
y
x +1
z = 1 +
z
1 13
1 13
y + x + 16 + x − y = x + x + 16
97
30. x 2 + y 2 =
36
x < 0
y > 0
32.
2
x
2008 2007
+
− 20082 − x 2 = 2008
x
2007
> 2x
om
28. x +
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29. x 2 +
35
>
x 2 − 1 12
x
)
(
38. 3 x 2 + 9 x 2 + 3 + ( 4 x + 2 )
(
4
( 1 + x + x + 1) = 0
)
kh
o
x + y − 3 x + 2 y = −1
40.
x + y + x − y = 0
42.
(
x + 8 x .log 2 x
2 x − 2 = 3 y − 3x
41. y
y
2 − 2 = 3x − 3
)
4
2
−3x 2 − 5 x + 2 + 2 x > 3x.2 x -3x 2 − 5 x + 2 + ( 2 x ) .3x
3
43. ( 2cos3 x + 6cos x + 1) = 162cos x − 27
45.
47.
2
x
x + 8 x = + 8log 6
2
ng
39. log 22 x + 4 x.log 6
oc
)
bo
cu
(
.c
2
x
33. ( log 2 x ) + x log 7 ( x + 3) = log 2 x + 2log 7 ( x + 3)
2
y + y2 + 9
2
2
( x − y ) x + y + xy − 2 = 6ln
x + x2 + 9
34.
3
2
x − 2 x + 1 = y
1 + x
x 4 − 16 y 4 − 1
cos x − cos y
=
1 + y = e
y
36.
35. 8 x
x 2 − 2 xy + y 2 = 8
2
y = 1 − 2x − x
1 + log 3 ( x + 3)
1
>
36.
37. cos5 x + cos x = sin 3 x − cos x
x +1
x
44.
2 x − 1 + x 2 − 3x + 1 = 0
2 x + 3 + x + 1 = 3x + 2 2 x 2 + 5 x + 3 − 16
3
x + 7 =1+ x
48. ( x + 1) log32 x + 4 x log3 x − 16 = 0
( x − y ) x 2 − y 2 = 3
49.
2
2
( x + y ) x + y = 15
x 2 + 2 x ( 3x + y ) = 18
50.
x 2 + 5 x + y − 9 = 0
51. e x = 1 + ln ( x + 1)
52.
(
(
)
)
(
(
)
)
3
1 + x + 1 = x3 + 2
2
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xy − 18 = 12 − x 2
2
6 x − 3xy + x + y = 1
53. 2
54.
y2
2
x + y = 1
xy = 9 +
3
x + y −1
4
+ 3.42 y −1 = 2
x
x
55. 4 + ( x − 12 ) 2 + 11 − x = 0
56.
x + 3 y = 2 − log 4 3
x
π π
+ cos x = 2 trên − ;
2 2
57.
61.
60. 15 x5 + 11x3 + 28 = 1 − 3x
x ( y − 2 ) = ( x + 2 )( y − 4 )
62.
( 2 y + 7 )( x − 3) = ( y + 3)( 2 x − 7 )
oc
(
3
)
= 2 + 1 − x2
bo
cu
(1 + x )
4 − 3 10 − 3 x = x − 2
63. x 4 = 4 4 4 x + 1 + 1
64. 2cos 2 x + 2 3 sin x cos x + 1 = 3 sin x + 3 cos x
(
)
67. x x 2 − 2 = 3
69. 16 x3 − 24 x 2 + 12 x − 3 = 3 x
71. cos6 x − cos 4 x = 4 (1 + cos3 x )
68. x3 − 3x = x + 2
70. 2log 7 t = log 3 ( 2 + t )
2
1
1 x −1
− 1− >
x
x
x
x3 + x ( y − z )2 = 2
2
59. y 3 + y ( z − x ) = 30
3
2
z + z ( x − y ) = 16
2 2
2
x y − 2 x + y = 0
58. 3
2
2 x + 3 x + 6 y − 12 x + 13 = 0
3
65. 1 + 1 − x 2 (1 − x ) −
x +1
3
=x−
66.
2
x +1 − 5 − x
x−
om
2
.c
57. e tan
2
on
g
1 3
1 81 2
72. sin 3 x +
+ cos x +
= cos 4 x
3
sin x
cos3 x
4
73. sin 4 x − cos 4 x = 1 + 4 ( sin x − cos x )
74. x3 +
2 3
(1 − x )
= x 2 (1 − x 2 )
75.
kh
4 x 2 − x + 10 + 2 x = 3 3 2 x 2 − x 3 + 9 x 2 − 4 x + 4
1 2 x + y
8 xy
2
2
x
+
y
+
=
16
4 x +
= 2
4
x
+
y
x
+
y
77.
76. 2
3
2
x + 2x = x + x − y
4 1 2 x + y
8 y 3
y 4 − x + y = 1
3y 4 2
x
xy − x + y = 3
2 + 6 y = y − x − 2 y
78. 3
79.
2
3
4
x
+
12
x
+
9
x
=
−
y
+
6
y
+
5
x + x − 2 y = x + 3y − 2
2
2
3
4
81. 3 x + 6 + x − 1 = x 2 − 1
80. 4 x + x + 1 = 1 + 5 x + 4 x − 2 x − x
3
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