SƠ
̉
GIA
́
O DU
̣
C – ĐA
̀
O TA
̣
O CÔ
̣
NG HO
̀
A XA
̃
HÔ
̣
I CHU
̉
NGHI
̃
A VIÊ
̣
T NAM
VI
̃
NH LONG Đô
̣
c lâ
̣
p – Tư
̣
do – Ha
̣
nh Phu
́
c
------------------ ------------------------------------------
Năm ho
̣
c 2008 – 2009
Môn thi : TOA
́
N
Thơ
̀
i gian la
̀
m ba
̀
i : 180 phu
́
t
!
"
!#
$%
"
&''
"
!
(#)
!*
"
*#
+,(+#*
-
(
./
(
( ) ( ) ( )
f x y f x f y , x, y R+ = + ∀ ∈
0
#*1
-
2$%
"
( )
n
u
'
"
!
(#34
0 1
n 1 n 2
n
u 1 ; u 2
u u
u ;n 2,3,.....
2
− −
= =
+
= =
$%
"
#
(5+%
(56.
"
+!.
1
-
2$%
"
( )
n
u
)
+
"
(#
n
n
lim u
→+∞
77
#8
"
(5(#,9
(5
"
.(:
$%
"
+8
(#(!#9
-
()
:
$%
"
+#8
!:4
"
(#4(7+#
;#84(5
+,
(#
( ) ( )
n 2 n 1 n 2
n 1 x 3 n 2 x a 0
+ + +
+ − + + =
)%(5#
7
,*(5$%
"
<#*
!$(#!*
"
7#*
!$(#5*
=>#*
!$(#/#
"
)
?#*
!$(#+,.(53
(#
@*
"
3*(#.!
"
!#!#$%
"
#*
!$(#*
"
+#
(#0+%
=%
-
+%
?#*
!$(#$*!#*4
%
-
+%
.!*
"
#*
!
$(#5*
)
"
+(#A
"
+0#*
!$(#/#
"
@
>7
#*+5
"
!B).%(5+
!*
"
BC)
D:
#84
(5+,.(5+.2
"
(@E9
+BCF
=DF(@*
,:
3
"
(/
"
(#84
(5+,*
((%
+
"
;+5
"
!B@#8
"
(5(#,9
(5
2
2 2
r 1
m n 20
<
+
>7
%
"
(84
(5+#9
(5
1 2 3 4
d ,d ,d ,d
%%
+$*(5$*(5)
/#%(5!*
"
384
(5+#9
(5(
*
(9
+,(!.
(5%
+9
+;#9
(5@G%
+9
+;#9
(5!9
"
+!#.
"
(5+#H*+#8
"
+8
+
B===I@G%
+9
+
;#9
(5
J
!9
"
+!#.
"
(5+#H*+#8
"
+8
+
/ / / /
A ,B ,C ,D
@#8
"
(5(#,9
(5#/#%
"
+8
"
1
(I
J
B)
/ / /
DA B C
!*
"
+#
+
"
!#39
(5(#.@
KKKKKKKKKKKKKKKKKKKKKK
"
KKKKKKKKKKKKKKKKKKKKKK
9#*
!0LL?M0LLN
EB
"
B
"
GB
"
B
I E
G
@L
OA
(:84
+:A
"
2
*#
#)
"
!.
+#H*3
"
(')
2=+84
!
( ) ( )
/ /
f x y f x , x, y R+ = ∀ ∈
0
( ) ( )
/ /
f x y f y , x, y R+ = ∀ ∈
7
@>
0M7
( ) ( )
/ /
f x f y , x, y R= ∀ ∈
( )
( )
/
f x const
f x ax b
⇒ =
⇒ = +
1.5
#2
( )
f x ax b= +
)
*+84
!3FL
PA
2&'F'=
x R∀ ∈
=:
$%
"
+#8
!+.
22
"
1.0
0 4.0
8
n n 1
n 1
u u
u ; n 1,2,3,....
2
−
+
+
= =
+!*
"
n 1 n n 1
2u u u
+ −
= +
( ) ( )
n 1 n n n 1
2 u u u u
+ −
⇒ − = − −
( )
n 1 n n n 1
1
u u u u
2
+ −
⇒ − = − −
1.5
QH
"
+1
-
2$%
"
( )
n
v
'
"
!
(#34
n n n 1
v u u ,n 1,2,3,......
−
= − =
+!*
"
n 1 n
1
v v
2
+
= −
I**
"
( )
n
v
:
%
+!A
"
;$%
"
(#A()4
"
1
1
v 1 , q
2
= = −
1.0
( ) ( ) ( )
n n n 1 n 1 n 2 1 0 0
u u u u u ...... u u u
− − −
= − + − + + − +
n
1
n
n n 1 1 0 0
1
v 1
2
2 1
v v ..... v u u 1 1
1
3 2
1
2
−
− −
÷
÷
÷
= + + + + = + = − − +
÷
÷
÷
− −
÷
1.0
n
n
5
lim u
3
→+∞
=
0.5
7 3.0
QH
"
+#
$%
"
( ) ( )
n 2 n 1 n 2
y n 1 x 3 n 2 x a
+ + +
= + − + +
=)4
"
(:
$%
"
+8
(#(!#9
-
()
:
$%
"
+#8
!:4
"
(#4(7=+!*
"
( ) ( ) ( ) ( ) ( ) ( ) ( )
/ n 1 n n
y n 1 n 2 x 3 n 2 n 1 x n 1 n 2 x x 3
+
= + + − + + = + + −
1.0
( )
( )
n 2
/
n 2 n 2
x 0 y a
y 0
x 3 y a 3
+
+ +
= =
= ⇔
= = −
(53
"
(+#( @L
8
=+!*
"
n 3 n 2
CT
y y a 3 0 , x R
+ +
≥ = − > ∀ ∈
)
R7
.2,2RL=
x R∀ ∈
I**
"
;#84(5+,
(#
( ) ( )
n 2 n 1 n 2
n 1 x 3 n 2 x a 0
+ + +
+ − + + =
)%(5#
+,(
7@L
!#*
(?#*
!$(#+#*
2.!A
.
3
)
*+%
=?#*
!$(#!*
(:
+
*+#
(#
+%
0@
#*
(5*
=0/#
"
=>+,.(53
(#!*
"
1 2 5
3 5 8
C C C
!
"
!#
#*
(5*
=7/#
"
=+,.(53
(#!*
"
1 3 4
3 5 8
C C C
!
"
!#
#*
(05*
=0/#
"
=+,.(53
(#!*
"
2 2 4
3 5 8
C C C
!
"
!#
#*
(05*
=7/#
"
=7+,.(53
(#!*
"
2 3 3
3 5 8
C C C
!
"
!#
2.0
PA
2!*
"
1 2 5 1 3 4 2 2 4 2 3 3
3 5 8 3 5 8 3 5 8 3 5 8
C C C C C C C C C C C C 7560+ + + =
!
"
!#
@L
> 7@L
E9
+F=BF3=BF!=+!*
"
2
2 2 2
a
AE m b
4
= = +
)
2
2 2 2
b
BF n a
4
= = +
.2,
2
2 2
5c
m n
4
+ =
2 2 2
1 4
m n 5c
⇒ =
+
0.75
ABC
1 a b c
S pr ab r
2 2
∆
+ +
= ⇔ =
2 2
ab ab
r
a b c
a b a b
⇔ = =
+ +
+ + +
0.75
!*
"
( )
2
2 2
a b a b+ > +
2 2
2 2 2 2
a b a b
a b a b 2 a b
⇒ + > +
⇒ + + + > +
2 2 2 2
1 1
a b a b 2 a b
⇒ <
+ + + +
0.75
G9
+/#
"
!
2 2 2 2
2 2 2 2
a b ab a b c
ab r
2 4
a b a b 4 a b
+ +
≤ ⇒ = < =
+ + + +
.2,
2
2
c
r
16
<
0
8
)
0+!*
"
2 2
2 2 2
r c 4 1
.
m n 16 5c 20
< =
+
0.75
< 7@L
*
FB
I
I=
/ / / / /
O A C B D= I
I*II
J
JJ
J
((
( )
( )
( )
( )
/
/
/
/
d D , ABC
DD
OO
d O , ABC
=
)
( )
( )
( )
( )
/ / /
/
/
/ / /
d D, A B C
DD
OO
d O, A B C
=
.2,
/ /
/
/
D ABC O .ABC
DD
V V
OO
=
)
/ / / / / /
/
/
D.A B C O.A B C
DD
V V
OO
=
1.0
E9
+
( )
( )
/ / /
h d BB , ACC A=
!*
"
( )
( )
/ /
h d B, ACC A= =
( )
( )
/ / /
d B , ACC A
/ / /
O .ABC B.O AC O AC
1
V V h.S
3
∆
= =
0
/ / / / / / / /
O.A B C B .OA C OA C
1
V V h.S
3
∆
= =
7
1.0
E9
+1FBB
J
=
J
+#
/ / /
/
O AC OA C
1
S S OO .d
2
∆ ∆
= =
8
=0=7=$.2,
.;#
!#8
"
(5(#
1.0