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5
5, , -, 2009 .
1. (, 2014 ) a, x4 + (a 5)4 = |x+ a 5|+ |x a+ 5|
.
3;7
2. (-, , 2014 ) a,
loga3 + 2x4
1 + x4+ loga
5 + 4x4
1 + x4> 1
x.
(1;8]
3. (, 2014 ) a, (x 1)2 21a+ |x 1|+ (1 x)2 + 2a1 = 4 + 4a . a.
a=1;x=1
4. (, 2013 ) a,
|x a2 + a+ 2|+ |x a2 + 3a 1| = 2a 3
, (4; 19).
[
3
2
;3
]
[6;+)
5. (, 2013 ) a,
7a
a 5 2|x| = 4|x| +
12a+ 17
a 5 .
{170}(2;5)
1
-
6. (, 2013 ) a,
a2 10a+ 5x2 + 25 = 4|x 5a| 8|x|
.
{5}
[
1510
2;15+10
2
]
7. (, 2013 ) a, sin2 x+ 2 cosx+ a = sin2 x+ cosx a
(pi2; pi] .
(;0]
{
1
4
}
8. (, 2013 ) a,
x2 + (a+ 7)2 = |x 7 a|+ |x+ a+ 7|
.
9;5
9. (, 2013 ) a,
ax+3 2x x2 = 4a+ 2
.
[
2
3
;
2
7
)
{0}
10. (, 2013 ) a,
(4 cosx 3 a) cosx 2,5 cos 2x+ 1,5 = 0
.
[;6][0;+)
11. (, 2013 ) a,
log1x(a x+ 2) = 2
, [1; 1).
[
5
4
;1
)
(1;1]
2
-
12. (, 2013 ) a,
| cosx+ 3 sinx+ a| = a 3 cosx sinx
(pi;
3pi
2
].
(1;1]
13. (, 2013 ) a,
1 2a1 + x2 + a(1 + x2)1 + x2 21 + x2 = 3
.
(;3)[4;+)
14. (, 2013 ) a,
4x2 a 21x2 + a21x2 1 = 3
.
(;3)[2;+)
15. (, 2012 ) a, (1; 2) - x, a+
a2 2ax+ x2 6 3x x2.
(3/2;+)
16. (, 2012 ) a, x2 + ax+ 1x2 + x+ 1 < 3
x.
(1;5)
17. (, 2012 ) a,
f(x) = 4x2 + 4ax+ a2 2a+ 2
1 6 |x| 6 3 6.
(;2]{0}[7+
17;+)
3
-
18. (, 2012 ) a,
2
x+ 1= a|x 3|
[0; +) .
(1/2;2/3]
19. (, 2012 ) a, 5x 3 = ax 2
(0;+) .
(6/5;5/4)
20. (, 2012 ) a,
|x2 8x+ a+ 5| > 10
[a 6; a].
[
19
45
2
;
7+
69
2
]
21. (, 2012 ) a, 1 2x = a 7|x|
.
[7/2;25/7)
22. (, 2012 ) a,
x10 + (a 2|x|)5 + x2 2|x|+ a = 0
.
(0;1)
23. (, 2012 ) a |x22x3|2a = |xa|1 ?
025/12
24. (, , 2012 ) a |x + a2| = |a + x2| ?
0;1;
1+
2
2
;
1
2
2
4
-
25. (-, , 2012 ) a,
(y 2x)(2y x) 6 0,(x+ a)2 + (y a)2 = |a+ 1|
5
.
1/21/4
26. ( , 2012 ) a,
ax 1 =8x x2 15
.
[
1
5
;
1
3
)
{
8
15
}
27. (, , 2012 ) a, -
y2 + a = 4 cos x,y + z2 = a,
(a 2)2 = |z2 2z|+ | sin 2x|+ 4 , - a.
(
pi
2
+pin;0;0
)
a=0,nZ;(2pik;0;2)a=4,kZ;a
28. (, 2011 ) a, f(x) = 4ax+ |x2 6x+ 5| , 24.
(
3
29
2
;
3+
29
2
)
29. (, 2011 ) a, {x2 + (4a+ 5)x+ 3a2 + 5a < 0,
x2 + a2 = 25
.
(
5
2
2
;3
)
(
0;
5
2
2
)
30. (, 2011 ) a, {
(|x| 5)2 + (y 4)2 = 4,(x+ 2)2 + y2 = a2
.
65+23
5
-
31. (, 2011 ) a,
x2 8x = 2|x a| 16
.
7/2;4;9/2
32. (, 2011 ) a, {(x 4)2 + (y 4)2 = 9,y = |x a|+ 1
.
73
2;4;1+3
2
33. (, 2011 ) a, {y =12 + 4x x2 + 2,
y =16 a2 + 2ax x2 + a
.
[2;2)(2;6]
34. (, 2011 ) a, (|x| 4)2 + (|y| 4)2 = 4,y = ax+ 1,
xy > 0
.
6
21
6
;
10+
37
6
35. (, 2011 ) a, {5 2|x| + 6|x|+ 7 = 5y + 6x2 + 4a,x2 + y2 = 1
.
7/4
36. (, , 2011 ) b,
x+ 3 4x 1 +x+ 8 6x 1 = b
[2; 17].
[1;3]
6
-
37. (-, , 2011 ) a, {
4|y 3| = 12 3|x|,y2 a2 = 3(2y 3) x2
.
(4;3)
{
12
5
}
{
12
5
}
(3;4)
38. (, 2011 ) a, {|x+ 2y + 1| 6 11,(x a)2 + (y 2a)2 = 2 + a
.
2;3
39. (, 2010 ) a, y2 + xy 4x 9y + 20 = 0,y = ax+ 1,
x > 2
.
(1;0][1;3/2)
40. (, 2010 ) a,
||x2 2x 3| x2 + 2x 5| 6 13
(a2 a
2
) x2 + 2x+ 1
.
(3/2;2)
41. (, 2010 ) a, f(x) = x2 7|x a| 3x [6; 6] .
(;2][4;+)
42. (, 2010 ) a,
36x (8a+ 5) 6x + 16a2 + 20a 14 = 0
.
(7/4;1/2]
7
-
43. (, 2010 ) a, f(x) = 4ax+ |x2 8x+ 7| 1.
(
;
1
4
)
(
4+
6
2
;+
)
44. (, 2010 ) a,
f(x) = x2 2 x a2 6x .
(
2;
2
)
(
2;2
)
45. (, 2010 ) a, - x2 + (5a+ 3)x+ 4a2 6 4 ax(x 4 a) 6 0.
5/3,3/2,1,1
46. (, 2010 ) a,
y =x2 2x+ a
6 + x2
.
(1;11)
47. (, 2010 ) a,
cos
(10x 2x2 a
3
) cos(2x+ a) = x2 8x a
.
16
48. (, 2010 ) a,
64x+a 4x25x+4a = x2 8x+ a
.
(16;+)
49. (, 2010 ) a,
5 x+ |x+ a| 6 3 .
(8;9/4](2;4)
50. (, , 2010 ) a, -
y = 9 + 7x 3|ax+ 2|+ |ax+ 5|+ |x+ 1| .
2
8
-
51. (, 2009 ) a, x ax ax 2 + 2a > 0,x 8 > ax
.
[1;3]
52. (, 2009 ) a,
cos(
a2 x2)= 1
.
(8pi;6pi)(6pi;8pi)
53. (, 2009 ) a,
3x+ |2x+ |a x|| = 7|x+ 2|
.
(;12][8;+)
54. (, 2009 ) a,
|2x a|+ 1 6 |x+ 3|
1.
5/2;19/2
55. (, 2009 ) a,
f(x) = x2 |x2 + 2x 3| a
.
(7/2;1)
9