- -
2011.
1
( ) ( )
n
n
f x b a af x b
,a b R
(1).
( ) ( ( ) ) ( ) ( )
n
n
g x af x b g x b af x
(2).
( ) ( )
nn
f x b ag x
(3)
( ) ( )
( ) ( )
.
Vy ta có h :
3
3
x 1 2y
y 1 2x
. Tr a h:
3 3 2 2
x y 2(y x) (x y)(x xy y 2) 0 x y
(Do
2 2 2 2
y3
x xy y 2 (x ) y 2 0
24
) Thay vào h ta có:
3 3 2
x 1 2x x 2x 1 0 (x 1)(x x 1) 0
- -
2011.
, , ( )a b f x
.
()fx
.
.
()fx
.
Ta
22
2 4 2( 2 )x x x x
=
2 2 2
2 4 2( 2 1) 2 2( 1) 2x x x x x
.
()fx
= .
()fx
2
(x 1) 2
2(x 1) 2
.
Ta có h :
2
2
1
t 1 y
2
1
y 1 t
2
ty
1
(t y)(t y ) 0
1
2
yt
2
1 17 3 17
tx
44
(tha
x3
).
- -
2011.
3
*
2
2
1t
(t ) 1
4t 2t 3 0
1
22
yt
1
1
2
t
t
2
.
Gi
2
x x 1000 1 8000x 1000
.
1
x
8000
2
1000 1000 1 8000x x x
.
()fx
.
.
PT
2
4x 4x 4000 4000 4000(2x 1) 3999
2
(2x 1) 4001 4000 4000(2x 1) 4001
()fx
=
. Do
u v 4000 0
nên T (2) ta có:
uv
c:
2
u 4000u 4001 0
u0
- -
2011.
4 u 4001 x 2001
. Vm:
x 2001
.
t
2
t 2x 1;y 2t 3x y 3x 2t
và
y0
.
Ta có :
2
2
t 3x 2y y t
(t y)(t y 2) 0
y t 2
y 3x 2t
.
*
2
2
t2
x
2
7
x
4
.
Vm:
71
x ;x
44
.
Gi
22
4x 11x 10 (x 1) 2x 6x 2
t
u 2x 3; v (x 1)(2x 3) x 1
,
Ta có h
2
2
u x 1 (x 1)v
v x 1 (x 1)u
22
u v (x 1)(v u) (u v)(u v x 1) 0
*
2
u v u x 1 (x 1)u
2
(2x 3) x 1 (x 1)(2x 3)
2
2x 6x 7 0
m.
*
( ) (3 )f x x c
.
PT
3 2 2
3
27 54 27 153 27 9( 3 21 5)x x x x x
. (*)
- -
2011.
6
Tuy nhiên .
.
.
c
b
=
).
b
=
2
81x
.
3
3 2 2
10 2 7 23 12x x x x x
.
32
( ) ( 2) ; 7 22 10, 1f x x b x x a
.
3
22
3
2; 7 23 12 ( 2) ( 7 22 10)u x v x x x x x
.
32
33
32
22
- -
2011.
7
3 2 2
(*) 5 11 4 0 ( 4)( 3 1) 0
4
35
2
35
2
x x x x x x
x
x
x
7 23 12xx
.
4tx
. Thay
3
2
7 23 12 6xx
=
t
, do
4t
2
.
3
2
2 7 23 12t x x
.
3 2 2
32
3 3 2 2 2 2
6 12 7 23 4
2 7 23 12
3
[( 3) ] 3 4 0(**)
( 3) ( 3) 3 4 0
24
x x x
x x x
x
t x x
t x t x x
- -
2011.
8
3 5 3 5
4; ;
22
x x x
.
a
""
a
""
B8: Gi
3
22
1
8x 13x 7 (1 ) 3x 2
x
.
.
3
3 2 2
8x 13x 7x (x 1) 3x 2
- -
2011.
9
*
3
2 3 2
u v 2x 1 3x 2 8x 15x 6x 1 0
2
x1
(x 1)(8x 7x 1) 0
1
x
8
9: Gi
2 2 2
3
7x 13x 8 2x . x(1 3x 3x )
.
. Tuy nhiên .
2
x
.
3
2 3 2
7 13 8 1 3
23
xx
x x x
. (*)
1
t
x
.
3
3 2 2
8t 13t 7t 2 t 3t 3
.
3
2
u v 2t 1 t 3t 3
32
8t 13t 3t 2 0
2
(t 1)(8t 5t 2) 0
2
t1
t1
5 89
t
8t 5t 2 0
16
. .
10:
22
2 2 1 (4 1) 1x x x x
.
.
2 2 2
1 1 1(*)x t x t
.
22
2( 1) 2 1 (4 1) 2 (4 1) 2 1 0t x x t t x t x
. (**)
Xem (**
22
1
2
(4 1) 8(2 1) (4 3)
4 1 4 3 1
1
42
(*)
4 1 4 3
21
4
x x x
xx
t
xx
4
.
3
3 4 0
x
t x x x
xx
x
x
xx
- -
2011.
11
t
2
3 5 3 1 4x x x x
.
t
t
.
3:
22
6 14 98 35 6x x x x
2 2 2
6 35 98 6 14 6 14 .t x x x t t t x
K
2
2
6 14
6 14
x x t
t t x
57
x cos ;x cos ;x cos
9 9 9
.
:
3
3
1 3 3 1xx
.
2 4 8
2cos ;2cos ;2cos .
3 3 3
:
2
3
2 4 , 1
2
x
x x x
.
3 17
.
:
3
3 2 2 3
2 10 17 8 2 5x x x x x x
3
3 2 2 2
1 4 2 7.
4
x
x x x x x
2
32 32 2 15 20x x x
. (
.
1 9 221
;
2 16
x
G
2
2
4 3 5
2 2 5
2
xx
xx
.
S= {
5 1 3 5
;
24
}.
3
22
2 6 5 3 3 2x x x x
.
3 5 3 5
;
22
}.
2011
xy
yz
zt
tx
Minhduy_k16_THD@yahoo. com.