MỘT SỐ ĐỀ TUYỂN SINH VÀO 10 CO ĐÁP ÁN
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (731.02 KB, 24 trang )
Đề 106
Bài 1: (4 điểm
x x x
x
x x x x
−
+ −
÷ ÷
÷ ÷
−
+ −
!"
#$
Bài 2: (5 điểm%&'()*
+ ,
,
y
x xy y x y
x y x y
+ − − + + =
+ + + − =
%&()*
- -
.
x x
x x
x x
− −
+ =
÷
+ +
Bài 3: (3 điểm #/0120345:
6060
0
Bài 4: (2 điểm#/20272.&4860876606,
39:
6;0
6<7
6
Bài 5: (6 điểm)=>8?@ ABC:DB)=>.ECFGC1
)=5G
⊥
?:H:2AIJ(0JFK2FAL)=>8K2MBJ(.NO0KP
?FAB?:MQM)RHSABT.
U?:.?TVWX2EY#0KMWZC/.
USGC1C)=>/.
J?: 240A[FG'[FK?39.
39Y.
Đề 107
Bài 1(4 điểm)
-
-
< - - -
-
- - -
- -
x x x
A x
x x x
x
+ +
= − −
÷
÷
÷
÷
+ + +
−
!"
A
.
01
x
A
\01.
Bài 2(5 điểm)
%&'()*
- - -
0 7 < 8
0 7 8
0 7 8-
+ + =
+ + =
+ + =
%&()*
--<
-
=++++
8
Bài 3(4 điểm)"](#/01G)*8@0#
+
+
yx
x
MB#/01G)*.
2027MB#/G)*&407
≥
60676ML96067
Bài 4(2 điểm)#/G)*22&4^V'.U
1
5 5 5 5 5 5
ab bc ca
a b ab b c bc c a ca
+ + ≤
+ + + + + +
Bài 5(5 điểm)
)=>8?@ AB)=5GVWZ?P)=>8?H:ABK.E
CF_0`1)=5GABDB)=>8?AIJ(0JFaABFAL)=
>8?8F2aMBJ(.
U
.MN MP MA MB= =
NbA[F1)=5G#Fa?MBAW.
UO)=>CJ(ABO)=>HJ(Fa
MQM)RH01)=/VFGC1)=5G.
8,<.
+ ,
,
8 + ,
,
8 8 ,
,
,
,
,
,
+
A
-
+
x xy y x y
x y x y
y x y x x
x y x y
y x y x
x y x y
y x
x y x y
y x
x y x y
x
y
x
y
+ − − + + =
+ + + − =
− + − + − =
⇔
+ + + − =
+ − − + =
⇔
+ + + − =
+ − =
+ + + − =
⇔
− + =
+ + + − =
=
=
⇔
= −
= −
0
c\0'()*Y'8@@
-
@ d
+ +
−
÷
ecL≥AB0≥Y
x y x
x y y
≥
≥
⇒
0
≥8
60
60
6
60
≥
60
60$
60
60
ec\0≤]0≤
dcL0AB()*)R6060
0
0-0
d0d,⇒)*VWY
'01
dcLd0AB()*)Rd060
0
0-0
60d,⇒)*VWY
'01
dcL0AB()*)R6060
0
00d
dcLd0AB()*)Rd060
0
0d0,⇒0
dcL,0AB()*)R0,
fMH)R()*Y-'01820MB8,@,@82d@8d2
.Y860876606,g$860876606-+,
$:686087660
6;0
6<7
6
6766060760
680676687606
60
d0767
67
d76<
60
d06
h687606i
680d7
687d
680d
≥
,.:
.352≥
N995&0
0j7,
7d,
g$ 0d,
60676,
860876606,
$8@0@7@U8@d@d@d]8d@@@
+.Nk90?F⊥K
∆S?T ∆:?F$
OM
OK
OA
OH
=
$?:.?T?S.?F8
lm∆K?FAWHK1?K
?S.?F8
E8AB8#0:.?T
8VWX$
OA
R
OK
=
8VWXGYT/1?:
Y?ST;,
,
$SU1)=>)=V[?T/.
FK?Y)=mAWY1n
FK?
?F.K
$n39⇔?F39ABK39.
6?F39⇔F_AL:
6K39⇔K⊥?T⇔S_ALT⇔F_AL:
aJ?:
R
R
R
OK ==
@KKT
-
R
R
R =−
c\0n
FK?
.
RR =
8,o.Y
( )
- - - - ,@ - ,2 ,x x x x x+ + = + + > + > ∀ ≥
21^V':YpMB
( ) ( ) ( )
-
- - - - ,2 , - ,
-
x x x x x x x− = − + + ≠ ≥ ⇔ ≠ ⇔ ≤ ≠
( )
( )
-
-
-
-
< -
-
- - -
-
x
x x
A x
x x x
x
+
+
÷ ÷
= − −
÷ ÷
+ + +
÷ ÷
−
.
( )
( ) ( )
( )
< - -
- - -
- - -
x x x
A x x x
x x x
+ − −
÷
= − + −
÷
− + +
( ) ( )
( )
- -
- -
- - -
x x
A x x
x x x
+ +
÷
= − +
÷
− + +
( )
-
-
x
A
x
−
=
−
8
,
-
x≤ ≠
( ) ( ) ( )
- - -
-
- - -
x x x
A x
x x x
− − + − +
= = = +
− − −
cL
,x
≥
2:MB#/01
- - - ;
- -
-
-
x x
x x
x
x
= =
− = ± ⇔ ⇔ ⇔ =
=
=
8A
x
∈
Z
AB
,x
≥
.TY
A =
.6E8-6067
( )
-
0 7 <
⇔ + + =
6E8AB8-Y
( )
( )
-
- - -
0 7 0 7 ,
+ + − + + =
KJX)*)*)A^)R-8608067867,
6lm60,0AB8-)R7
20AB8)R,@0,
NY)R8@0@78,@,@
lm067,2&)*b)R8@078
@,@,
lm76,2&)*b)R8@078,@
@,
6c\0'()*1Y-'8@0@78,@,@
@8
@,@,@8,@
@,
\90MB'8
cL
,
<≤
--<--<
- -
=++++<++++
.a1AW'AL
,
<≤
cL$
--<--<
-
-
=++++>++++
a1AW'AL$ c\08Y'G09
(GqKr0#/G)*2027.Y6067
≥
-
- xyz
KJX)R86067
-
≥
o860676.r]6067$,
KJX)R8d<86-
≥
,
⇒
≥
<.)R%aa<V07
r]
+
+
yx
x
cLMB#/01G)*
68
06⇔
8
d0d8
lm-)=R(#SaJE8Y
8
d0d⇒
−=−
=
y
x
⇔
=
=
y
x
SaJE8Y
8
d0,2#0
01YV20V
ALVMB#/01G)*
S-aJ$E82Yj$,AB8jJ
1j≥
⇔≥
6$
EY⇒,g
d0g
d
0≤,.r^B0VW&0
c\0](#/01G)*8@0&4^MB8@AB8V@V
ALVMB#/01G)*.
.Y
+
6
+
868
d
-
6
j
-
6
86h8d
8
66
6
N
2
(a - b) 0; a,b,c > 0,
≥
1
2 2 2
(a - b) (a + ab + b ) 0
≥
n0
( )
5 5 2 2
a b a b a b+ ≥ +
.r5#&0V.
NY
( )
( ) ( )
1 1
2 2
5 5
1
ab ab c
ab a b ab a b c a b c
a b a b ab
a b ab
≤ = = =
+ + + + + +
+ +
+ +
88AY
)*bY
5 5
a
b
bc
a b c
c bc
≤
+ +
+ +
8
5 5
b
ca
a b c
c a ca
≤
+ +
+ +
8-
CEAJ8@8@8-Y
1
5 5 5 5 5 5
a b c
a b c
ab bc ca
a b ab b c bc c a ca
+ +
=
+ +
+ + ≤
+ + + + + +
N9st&0V
+.
YFaF8[9J(0JP
)RF:aABFaKuGH.
n0
.
MA MN
MN MP MA MB
MN MB
= ⇔ = =
rFa?MBAW)=m
OM ON R= =
NbFGbAW?:N2Gb)=>O?ZN2P8GHF.
EFAIJ(0JFaABF.Y
MN MO ON R= − =
21?aF
AWOHa.)*b2?FvAWOH.NYFa?MBAW.
KBMWY'A
OM R R= >
6YFaABFMBJ(0J8?21Fa?MBCJ()=>)=V[?F.
OMBS?F.n0OFw)=>)=V[?F2OMBS.
6Tx
OE AB⊥
2yMB:K8/.Tx
8 HL d⊥
Sz{{?y21SzMB)=
?yF2#0
HL OE=
8VWX.
6NY2VFC18GSMWG^8GCHVWX21SH01)=5
8G|{{8GAB8G|ZH?y.
Đề 108
Bài 1(4 điểm):
+
+
−
−
+
−
+
−
+
+
+
+
xy
x
xy
xxy
xy
xxy
xy
x
. !".
.
<
=+
yx
F:.
Bài 2(5 điểm)%&'()*
−=+
−=+
−=+
yzx
xzy
zyx
#/b202734
,,<
=++
zyx
AB
,,<
=++
zyx
U[9C#/2027U,,<.
}(Gq&()*#
x x x x
+ = +
+ − + −
.
Bài 3(2 điểm)2027$,&46067
%aa
x y z
y z z x x y
+ +
+ + +
Bài 4(4 điểm)%&()*'01
0
d
d0
08
](5?02)=58GY()*
( ) ( )
- 0
− + − =
8MB#/.V&E/"CJ)=58GMBML9.
Bài 5(5 điểm)
)=>8?@ )=V[:K/.SMBCH?K#
SKS?.TxGO0NAWYAL:KHS.%"yMBGC13K#y
VW_ALABK.a/:ALyPNH~.
{U:N
:~.:y
{[:~.:yjS:.SK•
{lA[yV&ESJO)=>HJ(
∆
N~yP9.
Đề 109
Bài 1(4 điểm) :
x x x
x x x x x
+ −
+ +
÷
÷
− + + −
AL
,2 x x〉 ≠
!":.
U,g:g.
Bài 2(5 điểm) %&'()*
-
-
-
; o o ,
; o o ,
; o o ,
y x x
z y y
x z z
− + − =
− + − =
− + − =
%&()*
-
j-
6;j;,
Bài 3(2 điểm)%&#f20MB#/G)*&45
,=+ yx
AB0
88
++= yxP
H39.3990.
Bài 4(4 điểm) '01()*
-
60
-
6<0.
#/b223466 U
- - -
a b c a b c
+ + ≥ + +
Bài 5(6 điểm)
. )=>O?2)=V[K .E1J(0J)=>
HK2AIJ(0J:8:MBJ(AL)=>.%"SMBJ:M1K2yMB
AB:S.
yMB:S.
[:S• ABV&G?.
.AW:KN8
∠
:
∠
N;,
,
ABN:K.%"SMBJN1
)=m:ABFMBHS.UKF
⊥
FN
8,.rV≥,@0≥,@.0≠.w0u!")R:
yx.
;
.
<
≤=⇒=+
yx
A
yx
⇒F:;⇔
;
-
==⇔== yx
yx
.lr2027≥
.aOAJ€()*ALY
−=+
−=+
−=+
-8
8
8
yzx
xzy
zyx
C82828-EAJY
( ) ( ) ( )
,
=−−+−−+−−
zyx
⇒
=−
=−
=−
z
y
x
⇒
=
=
=
z
y
x
.fMH90&4.c\007
MB''.
E&JY
zyxzyx ++
=++
,
=
++
−++⇔
zyxzyx
( )
,=
++
−++
+
+
⇔
zyxz
zzyx
xy
yx
( )
( )
,
=
++
++⇔
zyxzxy
yx
( )( )( )
,
=+++⇔
zyzxyx
⇔
=+
=+
=+
,
,
,
zy
zx
yx
⇔
=
=
=
,,<
,,<
,,<
x
y
z
TJM\c\0[9C#/2027U,,<
er]62d2dd
⇒
66d
)*8eDB
a b c a b c
+ + =
+ +
•VJZ&OY
( ) ( ) ( )
,a b b c c a⇔ + + + =
⇒
6,
, ,8 { x x x t m⇔ + + − = ⇔ =
]6,
,x x⇔ − − − =
8AWM[]6,
, , x x x x⇔ + − − = ⇔ − = ⇔ =
8MH
c\0()*Y'MB,
c2027$,Y(GqKrW#/AL#/G)*
x
y z+
AB
y z
+
)R
. .
x y z x y z x
x
y z y z
+ +
+ ≥ = =
+ +
8.)*bY
8 B 8-
y x z z x y
y v z
x z x y
+ +
+ ≥ + ≥
+ +
C86868-)R
( )
x y z x y x x y z
x y z P x xy z
y z z x x y
+ + + +
+ + + ≥ + + ⇒ ≥ + + − =
÷
+ + +
N9st&0
-
x y z
⇔ = = =
.c\0
-
x y z
⇔ = = =
.a\900,MB'.
cL20
≠
,8g$0
8
do860
8
⇒
jo(&MB()*#/01.
S0
jo
⇔
j
o
8 8 ox a x a⇔ − + =
o
x a
x x
x a
+ =
⇒ ⇒ = ⇒ = ±
− =
0d2)R0@0d.02)R0@0.
c\0()*Y'01MB8,@,@8d@@8d@d@8@@8@
cL"2)=58GVWZ/HC?8,@,.
•
2Y)=502GYV&E?J8GMB8.
•
-2Y)=5d2GYV&E?J8GMB8.
•
≠
2
≠
-8GPq?02?MQM)RH
: ,@
-
÷
−
AB
K @ ,
÷
−
.
SH?SAWYAL:K2AW:?K2Y
?: 2 ?K
-
= =
− −
( ) ( )
o
- +
?S ?: ?K
= + = − + − = − + = − + ≥
÷
.
n0
?S ?S ≤ ⇒ ≤
8-.
E82828-Y%za?SMB
2H)RVAB•V
o
.TJM\
o
.
+.
{:N
:y.:~
. 8
. . 8 2
AD AH AB htl
AE AI AH AB AIH ABE
=
⇔
= ∆ ∆
uGH
{Y:~.:yjS:.SK:N
jSN
:S
8?:6?S
8 6
-
R
<
;
R
{TxN
DI D⊥ ≡
PyKVmGBH‚
⇒
N~y‚CJ(8XY/,
,
⇒
)=>HJ(
DIE∆
_AL)=>HJ(N~y‚Y)=V[MB~‚
%"TMB~‚ABKN
⇒
TMBO)=>HJ(
DIE∆
⇒
STP9
HK BD⇔ ⊥
K≡
⇒
TN
- -
R
⇒
y
∈
8?@
AL8T@
- -
R
8y
∈
3K)=>O?
8,;.AL
,2 x x〉 ≠
.Y:
( ) ( )
.
+ − + + − − − −
+ + =
÷
÷
− + + − −
− + +
x x x x x x x x
x x x x x x
x x x
( ) ( )
.
− +
=
− + +
− + +
x x
x x x
x x x
AL
,2 x x〉 ≠
MWY:$,.zHY
+ + > ⇒ <
+ +
x x
x x
0:g.c\0,g:g
.CEAJ-()*)R86-
6
80d-
687d-
,8
F]V8⇒;
do6o0
-
;8
o
-
+−x
$,⇒0$,@)*b$,@7$,.
.lm≥-E8-⇒;7
jo7
-
do≥,⇒;787j-≥,⇒7≥-
)*b0≥ E8⇒07-
.lm,gg E8-⇒;7
do7
-
jog,⇒;787d-g,⇒7g-
E8⇒'()*AW'.c\0'Y'G098-@0-@7-
-
j-
6;j;,g$-
-
j;
6ojo,g$-
-
;
jo6o
-
d
-
6;
jo6o8-j
-
$
- -
-
-
x = = − +
+
8
680
68
60
680
6
r]02Y
60
860
j0,j
60
8
60
j80
8,j
j
d,
6,,
TY
6
d,6,8
j6<6,8
d66+8
j
6,8j
6+
n0≥+.r5&0V⇔60
,
AB0
E
O
P
C
B
A
H
c\039MB+V820
,
@
, −+
]
+−
,
@
,
.r]n60@0$^V'Q'Y'MBn
≥8e
)*4)*)*ALn
-
j-n6<n
-
j-n6<j-
8nj8n
6nd-6-8
lmOfFn
6nj-6860
6860j-06
60
j068606
( ) ( ) ( )
[ ]
,
≥++++− yxyx
c\0njABFMB)L#/G)*#/01/-.m)=R(#
S
=
=
⇔
=
=
⇔
=+−+
=−
-
--
y
x
P
S
PSS
S
]
=
=
y
x
S
=
=
⇔
=+−+
=−
<
+
-
-
P
S
PSS
S
AW'AVW&48e.
c\0()*Y'01MB8@@8@.
cL"#/bY
-
-
8 8 8 8 8 ,
x x x x x x x
− − = − + + = − + + ≥
÷
NY
- - - - - -
8 8 8 8 a b c a b c a a b b c c+ + − + + = − + − + −
- - -
8 8 8 8 8 8 a a b b c c a b c= − + − + − − − − − − −
- - -
8 8 8 8 8 8 ,a a b b c c= − − + − − + − − ≥
n0
- - -
a b c a b c+ + ≥ + +
.S]-8
- - -
-8 a b c a b c+ + ≥ + +
-8
- - -
8 8 a b c a b c a b c+ + ≥ + + + +
OABVAB!")A^Kr!
+.
Y:S{{K8A:S2K_AWYALK
yS S
K K
⇒ =
8
zHY:{{?8A:2?_AWYAL:K
1AW:SABK?uGH
:S S
K K?
⇒ =
8
FBK.K?1:S.yS0yMB:S.
Y:S
SK.S8 jSS
yS.K yS.K
:S .
K K
⇒ = −
÷
:S.K :S.K
.
K K
−
÷
K .:S 8 .K :S. .:S. ⇒ = −
K .:S .K .:S⇒ = −
( )
K .:S .K⇒ + =
FB
K G = −
1
:S . G
G
= −
%"aMBNS
FaMB)=
∆
NS$Fa
NABFa{{N
FB:K
N@:K{{N
$Fa:KABFa{{:K$:KFaMBB
$:a{{KF.EFa{{:KB:K
⊥
:N$Fa
⊥
:N
$aMBbO
∆
:FN$:a
⊥
FNA:a{{KFB:a
⊥
NF$KF
⊥
NF
Đề 110
Bài 1(4 điểm) :
( )
yx
xyyx
:
xy
yx
yx
yx
+
+−
−
−
+
−
−
!":
F:≥,
Bài 2(5 điểm) 202734'#
−=−−
−=−−
−=−−
xzz
zyy
yxx
-<-
-
-
-
-
-
.
%&()*#-86+86<86o
Bài 3(2 điểm) #/G)*@@3466
≤
U
,,;
<o,
a b c ab bc ca
+ ≥
+ + + +
Bài 4(3 điểm) %&#f22MBƒ#/b3422≠AB
,
=++=++
cba
cba
.
U
abc
cba
cba
=
++
++
<<<
39
:
0 7
0 0 7 7
+ +
+ + +
AL$,@0$,@7$,AB
0 07 7
+ + =
Bài 5(6 điểm) :KCJ()=>8?@ .rFC3K."~2T2S
•bMBJAWYF1:K@:@K.%"2wMQM)RMB:K@ST.
Fw⊥w.
MH
BC
MK
AC
MI
AB
=+
:K^.lA[F1KF:6FK6FHML9
Đề 111
Bài 1(4 điểm) Cho biÓu thøc:
−+
−++
+
−+= a
a
aaa
a
aM
-
a) T×m ®iÒu kiÖn ®Ó cho biÓu thøc M cã nghÜa.
b) Chøng minh r»ng biÓu thøc M kh«ng phô thuéc vµo a.
Bài 2(5 điểm) %&()*
- + + +
+ < +
x x x x
x x x x
− + − +
− = −
− + − +
%&'()*
-
-
x
x
y
y
x
x
y y
+ + =
+ + =
Bài 3(4 điểm) K#/@0@7&&'
<
-
=++
zyx
.lm60
67
-
.
.U
≥
606-7d-„
.39„.
Bài 4(5 điểm) f)=>8?2)=V[:KABJ(0JKf)=.1K
M902N8UƒKABN.:AB:NMQM)RP)=>HyAB‚@GO0:yAB
K‚PHF.S:‚ABKyPHa.U
Fa{{K.
N‚yCJ()R.
Bài 5(2 điểm) Y#/HMQM)RMB<@AB,.[V&EO)=
>HJ(JO)=>CJ(.
8,.rT
≠
≥
≥
yx
y
x
,
,
.:
yx
yxyx
:
yx
yxyx
yx
+
+−
+
++
−+
:
yxyx
yx
.
yx
yxyxxyyx
+−
+
+
−−−++
:
yxyx
xy
+−
N
,
≥
xy
2
,
-
>+
−=+−
y
y
xyxyx
$:
,
≥
+−
yxyx
xy
.KJX)*)*'Y
-
-
-
8 8
-
- 8 8 8
- < -
8 8 -8
x x y
x x y
y y z y y z
z z x
z z x
− + = −
− − = −
− − = − ⇔ − + = −
− − = −
− + = −
aOAJ-()*AL)R
8d80d87d86
806
876
d<8d80d87d
⇔
8d80d87d
[ ]
<888
++++ zyx
,
⇔
8d80d87d,.
⇔
]0]7
cL]0]70AB')R07.
c\0AL0734'4.
%&()*#-86+86<86o
g$;86+86<86o
r]06;]]06<.Y'd;
}(Gq8668
a
6
b
6
c
≥
;.Y
;
8 8 ;
8
a b c ab bc ca
ab bc ca ab bc ca
a b c a b c a b c
+ + + + + + ≥ ⇒ + ≥ ≥
+ + + +
+ + + + + +
8
F]VE8j
68j
68j
≥
,$66
≤
6
6
$66
8 ,,o ,,o
- <<;
- -
a b c
ab bc ca
+ +
≤ ≤ ⇒ ≥ =
+ +
8
E8AB8Y
,,;
<o,
a b c ab bc ca
+ ≥
+ + + +
G9&0V
.e66,$6d$86
-
d
-
$
-
6
-
6
-
d-86-
e
1 1 1
0
a b c
+ + =
$66,
e
<
6
<
6
<
8
-
68
-
68
-
8
-
6
-
6
-
j8
-
-
6
-
-
6
-
-
e66,$
-
-
6
-
-
6
-
-
-
NYe
<
6
<
6
<
8-
j
-
.6c\0
6 6 6 2 2 2
3 3 3
a b c 3a b c
abc
a b c 3abc
+ +
= =
+ +
6KJX)R
:6067
0 07 7
0 0 7 7
− + +
÷
+ + +
8
6)R6067
0 07 7≥ + +
$,8
6088-AB8)R:
≥
NYF:
0 7
0 07 7
= =
⇔
+ + =
6c\0:
0 7
-
⇔ = = =
+.FTSCJ(
⇒
·
·
·
·
·
·
BCM = HKM = BAM; HMK = BCA = BMA
⇒
∆
KF:
∆
SFT.
F]VF2FwMB0J
∆
KF:2
∆
SFT
⇒
MH
MB
MQ
MP
=
AB
·
·
BMH = PMQ
⇒
∆
KFS
∆
Fw
F]V
·
·
0 0
BHM = 90 PQM = 90 ⇒
⇒
w
⊥
Fw.
%&#f:
≥
:KY
MK
AK
MI
AI
MK
KCAK
MI
BIAI
MK
AC
MI
AB
+=
+
+
−
=+
8
8N
·
·
MBI = MCK
⇒
·
·
cotg MBI = cotgMCK
⇒
MK
KC
MI
BI
=
N
µ
µ µ
µ
1 1 1 1
C = A nªn cotgA = cotgC
⇒
MH
CH
MI
AI
=
8
µ
µ
µ
µ
2 1 2 1
A = B nªn cotgA = cotgB
⇒
(3)
AK BH
MK MH
=
E828AB8-#0
MH
BC
MH
BH
MH
CH
MK
AC
MI
AB
=+=+
%"NMBF:ALKNY
∆
FKN
∆
F:
· ·
·
·
( )
, BMD AMC DBM CAM= =
MB BD
MA AC
⇒ =
)*bY
MC CD
MA AB
=
NY
1
MB MC
MA MA
+ =
n0F:6FK6FF:
≤
c\08F:6FK6F V:FMB)=V[VYFMBK
81. §iÒu kiÖn:
−>
≠
,
- - -
-
a a a a a a a a a a a
M a a
a a a
a a a
+ + − + − + + − + − +
= + − + − = = =
÷ ÷
÷ ÷
÷ ÷
+ + +
KÕt luËn: biÓu thøc M kh«ng phô thuéc vµo a
.&fAB…(OAB]J(q
r^V'
,≠y
y
x
y
x
y
x
y
x +=
+⇔=++ -
-
8
y
x
y
x
y
x
y
x −=−
+⇔=++ -
-
8
C8AB8AJALAJ)R
,<
=−
++
+
y
x
y
x
,
-
=
−+
++⇔
y
x
y
x
=−+
=++
,
,-
y
x
y
x
⇔
( )
( )
=+
−=+
y
x
y
x
E8-AB8Y
⇔
=
−=+
<
-
y
x
y
x
=
=++
yx
yy
<
8e,-<
AW'
⇒
'AW'
A
B
E
C
D
O
F
I
r
r
r
1 0
6
8
E8AB8Y
⇔
=
−=+
-
y
x
y
x
=
=+−
yx
yy ,
@==⇔ yx
'Y'
@== yx
lm'860
6
-
0
d067
-
d-76-80
d06687
-
d-680d
687d
86
,
≥
G6$,
c\0
≥
606-7d-
(GqKrK/(#VY
8606-78
-
zyx
++
h8
-88 zyx ++
i.
+
+
-
zyy
≥
-8
-
.
. ++=
+
+
z
z
y
y
x
x
-<
$606-7
<<-<
=≥
$
< =−≥−++≥ zyx
r5&0V
-
-
<
-
===⇔
==
=++
==
zyx
z
z
y
y
x
x
zyx
zy
cH039-V07.
.:KaY
∠
:yK;,
,
8YCJ(Pf)=>g$:y⊥Ka8
∠
:‚K;,
,
8YCJ(Pf)=>g$K‚⊥:a8
E8AB8$FMBbO:Ka
$Fa⊥:K$Fa{{K8c_AWYAL:K
Y
∠
N‚y6
∠
K‚y
∠
N‚y6
∠
K:y;,
,
∠
K:6
∠
K:
∠
K:6
∠
K:y;,
,
$
∠
N‚y
∠
K:
TYN‚yY
∠
Ny6
∠
N‚y
∠
Ny6
∠
K:,
,
$Ny‚MBCJ(.
+. Y K
:K
6:
,
<
6
y
a
‚
:
K
F
:KAWH:21?H
0^KMBO)=>HJ(:K.
%"~MBO)=>CJ(:K2
N2y2‚MBJ()=>CJ(8~
1HK2:2:K2n2(2MQM)RMBG'[2
fA2V[)=>CJ(:K2Y
n(
<. < ,
.
+ +
=
⇒
.
•[9J(0JP2Y
KNK‚2Ny2:y:‚
n0KN6y6:‚(KN68y6:y(
KN6:(KN(j:(jj.
NY?N?Kj?N+j
•M`ddAW?~N2Y
?~
?N
6~N
6
+
⇒
?~
+
.c\0?~ =
+
.
Đề 112
Bài 1(4 điểm)
0 0
0 0
F
0
+ −
+ +
= + +
÷
÷
÷
−
− +
:
xy xy
.
^V'FAB!"F.
FAL
- = +
.
Bài 2(5 điểm) %&'(*
-
x y x y
x y x y
x y
+ + +
+ =
+ + +
+ =
8@0&4
( )
x y y x xy− + − =
Bài 3(2 điểm) 22MB#/bG)*.U
-
8 8 8 -8 .
a b c abc
+ + + + + ≥ +
+
Bài 4(4 điểm) #/VWO
2 2x y z
346067
≤
-
ML9
-8 .A x y z x y z= + + + + + + + +
%&()*'01
0
d
d0
08
Bài 5(5 điểm)
)=>8?@ AB)=58GVWZO?P)=>8?@ H
(O':2K.rF0C18GABUB)=>8?@ 2ZFVxJ(0J
FaABFL)=>8?@ 8a2MBJ(.
UFa?CJ()RC)=>2O)=>
Y.
F:.FKFa
.
lA[F#Fa^.
GlZ†[O)=>HJ(Fa.
8.6r]rTlr'
-
x y x y
x y x y
x y
+ + +
+ =
+ + +
+ =
MB8608606
,≠
6KJX()*
8 8
8 8
x y x y x y x y
x y x y x y x y
+ + + + + + +
+ = ⇔ =
+ + + + + +
8 8 8 8 x y x y x y x y⇔ + + + + = + + +
[ ]
( )
8 8 , , x y x y y y⇔ + + − + = ⇔ − = ⇔ =
600AB()*-60R
6r/J^V'ABVJM\''MB8@
6r^V1
≥
AB0
≥
8e
6 r]
@ a x b y= − = −
AL AB MB #/ VW O ^ V' ^ B D B
( ) ( ) ( ) ( )
a b b a a b
+ + + = + +
( ) ( )
( ) ( )
a b b a
a b
+ + +
⇔ =
+ +
b a
b a
⇔ + =
+ +
b a
b a
⇔ + =
+ +
8
6cL"@
@
b a
b a
≤ ≤
+ +
.NYE8#0
b a
b a
= =
+ +
8
%&8)R.NY0
6T20&4^V'^B.c\0](#/8@MB](#/Q.
22MB#/bG)*.U
-
8 8 8 -8 .
a b c abc
+ + + + + ≥ +
+
}(GqKrWd#-#/G)*Y
-
8 8 8 - 8 8 8
a b c a b c
+ + + + + ≥ + + +
÷
÷
-
-
8 8 8 8
a b c abc
+ + + ≥ +
+
8e.
zH•KrWd#Y
8 8 8
a b c a b c ab bc ca abc
+ + + = + + + + + + +
- -
- -
-
- - -
8 8
8
abc abc
abc abc
abc
≥ + + + = + ≥ +
+
8A666
-
- abc≥
c\08e)RKr4!AL"22$,.
r5&0VAB•V.
.#/VWO
2 2x y z
346067
≤
-
ML9
-8 .A x y z x y z= + + + + + + + +
}(GqKrKddd/(dV02)R
8 8 8 x x x x x+ + ≤ + + + = +
)*b:
8 8 8 y y y y y+ + ≤ + + + = +
8 8 8 z z z z z+ + ≤ + + + = +
KDA\0
-8
8 - 8 -8 < 8- 8
A x y x x y z
x y z x y z x y z x y z
= + + + + + + + +
≤ + + + − + + + + + = + − + +
⇒
:
≤
<
68-d
88 zyx ++++
≤
<
68-d
-;6-
8}(GqKrKddd/(dV0AB&J6067
≤
-
c\0ML9:MB;6-
207.
a\900,MB'.
cL20
≠
,
8g$0
8
do860
8
8
⇒
jo(&MB()*#/01.
S0
jo
⇔
j
o
8 8 ox a x a⇔ − + =
o
x a
x x
x a
+ =
⇒ ⇒ = ⇒ = ±
− =
•0d2)R0@0d
•02)R0@0.
c\0()*Y'01MB
8,@,@8d@@8d@d@8@@8@
+.
2NkZu.
Fa^V?F
Gw†[O)=>HJ(FaMB)=UG‡##AL)=5G8E
D1)=>.
Đề 113
Bài 1(4 điểm)
Cho biÓu thøc :
++
+
−
−
−
+
=
8
xx
x
xxx
xx
A
a) Rót gän biÓu thøc .
b) TÝnh gi¸ trÞ cña
A
khi
- +=x
Bài 2(5 điểm)
%&'()*
( ) ( )
( ) ( )
( ) ( )
8
- < 8
- - 8-
x y
y z
z x
+ + =
+ + =
+ + =
8~
Bài 3(4 điểm) 07AB6067
%aaK
<
60
<
67
<
22&4
a b c b c a c a b
c a b
+ − + − + −
= =
[
b c a
a b c
+ + +
÷ ÷ ÷
Bài 4(5 điểm) )=>8?Y)=V[:K ABC)=>Y8V
:2K.z90NCGO0K8NVK2.:NP3KHy2:PKyH
‚.
‚NyMBCJ(.
N:.NyNK.N.
-
·
CFD
·
OCB
. %"~MBO)=>HJ(‚Ny2~MB
J(0J)=>8?.
Bài 5(2 điểm)
:KYCGBHMBK2:2:KABAMB.
U
;
+ + ≥
− − −
8-
aO88AB8-Yh86806876-i
-<
86806876-<]86806876-d<
cL86806876-<'8~MB
,
- -
,
,
z
z
x
x
y
y
=
+ =
⇔ =
+ =
=
+ =
cL86806876-d<'8~MB
<
- -
z
z
x
x
y
y
= −
+ = −
⇔ = −
+ = −
= −
+ = −
c\0''MB8,@,@,AB8d@d@d<
a) Y 8d
68d
68d
≥, ∀22⇔
6
6
≥668
(Gq958Y
K
<
60
<
67
<
8
680
687
≥
0
60
7
67
⇔K
≥
0
60
7
67
⇔K
≥8
0
680
7
687
≥
0
.0
7
6
0
.7
60
7
.7
⇔K
≥
0
7
6
0
7
6
0
7
⇔K
≥8
0
7
68
0
7
68
0
7
≥
<
0
<
7
6
<
0
7
<
6
0
<
7
<
⇔K
≥8
-
0
-
7
68
0
-
7
-
68
-
0
7
-
≥
+
0
<
7
+
6
<
0
+
7
+
6
+
0
+
7
<
⇔K
≥807
+
.6807
+
.06807
+
.76067-8G07AB6067-
⇒K
-⇔07
EY
a b c b c a c a b
c a b
+ − + − + −
+ = + = +
#0
a b c b c a c a b
c a b
+ + + + + +
= =
lm)=R(eaJ66,
⇒
6d6d 6d
b c a
a b c
+ + +
÷ ÷ ÷
a b b c c a
a b c
+ + +
÷ ÷ ÷
8 c
a
−
.
8 a
b
−
.
8 b
c
−
abc
abc
−
d
eaJ66
≠
,
⇒
⇒
..
.
+. e
0 0
+ ≥
+
AL$,20$,
Y8d0
≥,∀20⇔
60
d0≥,⇔860
≥0
0
0 0 0 0
+
⇔ ≥ ⇔ + ≥
+ +
AL∀@0.
e}(Gq
( )
+ ≥ =
− − − + −
+ ≥ ⇒ + + ≥ + +
÷
− − − − −
+ ≥
− −
⇔ + + ≥ + + ⇔ + + ≥ + + + +
÷
− − − − − −
( )
;
≥ + + =
÷
8}(GqK(#V.N9U&0⇔
⇔
Đề 114
Bài 1(4 điểm)
< ,
:
- <
−
= − + − +
÷ ÷
− − + +
. !":.
.#:g.
Bài 2(5 điểm)
%&'()*
;
+
x y
x y
xy
xy
+ + + =
+ =
%&()*86
8
6
Bài 3(4 điểm)
.n/b0XAB34^V'
68-d
≥+.39
68-d
6<
8-d
.
.8#/G)*22J
≤
+
+
+
+
+ c
c
b
b
a
a
U
≤
Bài 4(5 điểm)
FaYY"AB:2K2MQM)RMBJAWYF2a2
1a2F2Fa.1H5:2:KMQM)RM90N2y#Ny##ALa.1
:KM90T#
·
·
=DMK NMP
.U
FNFy
FNyTCJ(.EY#0FMBO)=>BJ(YN:T
N:T.
Bài 5(2 điểm)
1)=>8?M90/:AB(O'.A[KABNC
)=>YA:KNYML9.
8.r^V'
,xy ≠
.S'4
h 8 8 i ; 8
8 + , 8
xy x y x y xy
xy xy
+ + + =
− + =
%&8)R
8-
8
xy
xy
=
=
E8ˆ8-Y
-
x
y
x y
xy
x
y
=
=
+ =
⇔
=
=
=
E8ˆ8Y
-
x
y
x y
xy
x
y
=
=
+ =
⇔
=
=
=
c\0'4Y'MB
8 @ 8@ 2 8@ 2 8@ { 2 8{ @ x y =
TAB!"ABAJ
.r]6{0.Y'
- - -+ ± +
r]0-dB4DB%aa
60
6<
0
Y20MB#/b0X34
-
+
x y
x y
+ =
+ ≥
E'1Y
;
+
x y xy
x y
+ + =
+ ≥
⇒8
60
68
60
60≥+6.;
⇒+8
60
680≥
K
E
B
C
A
N
M
P
D
F]V<8
60
6+80
≥,8
60
808
N95&0⇔8
60
+80.
CAJ8AL+8
60
6<80
)R
h8
60
680
i
≥h+8
60
680i
≥
08
60
680
≥⇔
60
6<
0
≥
r5&0
-
8 @ 8@
+
8 @ 8@
8 +8
x y
x y
x y
x y
x y xy
+ =
=
⇔ + = ⇔
=
+ =
NY39UH)R⇔]
.•&J
+
=
+
−≤
+
+
+
⇒≤
+
+
+
+
+ aa
a
c
c
b
b
c
c
b
b
a
a
N$,@$,1•95W#Y
, ,
8 8 8 8
b c bc bc
b c b c a b c
+ ≥ > ⇒ ≥ >
+ + + + + + +
8
)*bv)R
,
88
>
++
≥
+ ca
ac
b
8
,
88
>
++
≥
+ ba
ab
c
8-
E8@8@8-)R
888
.
.
cba
abc
cba +++
≥
+++
$
≤⇒≥ abcabc
$(
.GkGBFK:aCJ(
· ·
⇒ =MAB MNB
2F:CJ(
·
·
⇒ =CAM CPM
.
zHY
·
·
=BNM CPM
8_(qYaF
·
·
⇒ =CAM BAM
8
NNy{{a]VF:
⊥
a
⇒ ⊥
MA DE
8
E828
⇒ ∆
ADE
OH:
⇒
F:MBbNy
⇒
FNFy
NNy{{a1
·
·
=DEK NAB
2]VFa:KCJ(1
·
·
+ =
0
NMB NAB 180
·
·
⇒ + =
0
NMB DEK 180
•&J
·
·
=DMK NMP
·
·
⇒ + =
0
DMK DEK 180
⇒
FNyTCJ(
NF:MBbNy
⇒
MEA MDA
∆ = ∆
⇒
·
·
·
·
= ⇒ =
MEA MDA MEK MDC
.
c
·
· ·
·
= ⇒ =
MEK MDK MDK MDC
⇒
NFMB(OYNT2VJR(AL:FMB(ON:K
⇒
FMBO)=>BJ(YN:TN:T.
+.TW9XZ&#f:K
≤
:.%"K‡MB[ƒ
¼
ABC
⇒ =
AB' CB'
1/KM90:‡#K:‡K:
⇒ + =
AB BC CA'
Y
·
·
·
= =B'BC B'AC B'CA
8@
·
·
+ =
0
B'CA B'BA 180
8
·
·
+ =
0
B'BC B'BA' 180
8-@E82828-
·
·
⇒ =B'BA B'BA'
S:‡KK‡AB:KK‡U
⇒ =
A'B' B'A
Y
⇒ + = + ≥
B'A B'C B'A' B'C A'C
:K6K8K‡:6K‡VWXAK‡2:2/.N9
st&0VK_ALK‡.
SBB)*bJ"N‡MB[ƒ
¼
ADC
vY:N‡6N‡
≥
:N6N.N9
st&0VN_ALN‡.
⇒
A:KNML9VK2NMB[ƒ
»
AC
)=>8?
D'
B'
A'
O
C
A
B
D
Đề 115
Bài 1(4 điểm)
−
+
+
−
−
=
x
x
x
x
x
B
!K.
K+.
Bài 2(5 điểm) %&'()*
-
-
-
<
x
y
x
y
+ =
− =
%&()*'01
-
d0
-
d0
d-0d,
Bài 3(2 điểm) a, b, cMB#/bG)*0X3Y
-a b c+ + =
.
39
ab bc ca
a b c
a b b c c a
+ +
= + + +
+ +
Bài 4(3 điểm)
Bài 6(5 điểm)
)=>O8?)=V[:K20MBJ(0JHKAL)=>2NMBC)=
V[9V‰.%":AB:NAL0•bMBF2a.
UFNaMBCJ(C)=>.
U:.:F:N.:a
%"~MB)=O>HJ(FNa.T)=V[NZ0ZO?
~G01)=>B„
8+.r]
z
y
=
.S'4DB
-
-
-
-
x z
z x
+ =
+ =
( )
- -
- x z z x⇒ − = −
( )
( )
- ,x z x xz z⇔ − + + + =
x z⇔ =
8A
- ,2 2x xz z x z+ + + > ∀
.
EYY()*
-
- ,
x
x x
x
= −
− − = ⇔
=
c\0'4Y'
( )
8 2 8 @ 2 2x y = − −
)*4)*)*AL
-
0
-
60
6-06(1)
a\mU
- - -
, - 8 y x y y y y y≥ ⇒ ≤ + + + + = +
(2)
- - -
+ , - 8+ 8 y x y y y y y+ > ⇒ > + + + − + = −
(3)
E8AB8-#0
-
8 y −
g
-
≤
-
8 y +
2c0
∈Z
- - - -
- - - -
-
8 - 8
x y y y y y
x y y y y y
= + + + =
⇒ ⇔
= + + + + = +
- , 8
, ,
,
y y y vi y y
y y
y
+ + = = − ∈ =−
⇔ ⇔ ⇔
= =
=
Z
cL0d
⇒
d.cL0,
⇒
c\0()*Y]('01MB8d@dAB8@,
Y3(a
2
+ b
2
+ c
2
) = (a + b + c)(a
2
+ b
2
+ c
2
)
= a
3
+ b
3
+ c
3
+ a
2
b + b
2
c + c
2
a + ab
2
+ bc
2
+ ca
2
B a
3
+ ab
2
≥
2a
2
b 8(GqKrW#
b
3
+ bc
2
≥
2b
2
c
c
3
+ ca
2
≥
2c
2
a
Suy ra 3(a
2
+ b
2
+ c
2
)
≥
3(a
2
b + b
2
c + c
2
a) > 0. n0
ab bc ca
a b c
a b c
+ +
≥ + + +
+ +
; 8
8
a b c
a b c
a b c
− + +
⇒ ≥ + + +
+ +
r]t = a
2
+ b
2
+ c
2
2)Rt
≥
3.
n0
; ; -
-
t t t
P t
t t
−
≥ + = + + − ≥ + − =
⇒≥
N9U&0VAB•Va = b = c = 1. c\039MB
+.
<.∆:KFAWHK$
∠
KF:6
∠
K:F;,
,
.∆?:OH?
$
∠
:N
∠
K:F$
∠
KF:6
∠
:N;,
,
.∆:NAWH:
$
∠
:N6
∠
:N;,
,
$
∠
KF:
∠
:N
∠
:N6
∠
aN,
,
$∆FNaY
∠
aF6
∠
aN,
,
1CJ()=>
∆:KFAWHK2K⊥:F
$:K
:.:F 8∆:KaAWHK.KN⊥:a$:K
N.:a 8
E8AB8$:.:F:N.:a
•)RTE~S⊥0$~S{{?:8ABSaSF:S8∆:FaAWH:@SaSF
$
∠
a:S
∠
:aS
•O
∠
:N
∠
:FaB
∠
:aS6
∠
:Fa;,
,
$
∠
a:S6
∠
:N;,
,
$:S⊥N
F]V~?⊥N8??N@~?V[:S{{~? 8
E8AB8$:S~?MBB$~S?: 8 V[)=>8,
c\0VNZZO,~0C1)=5G{{00CV&U
