ĐỀ VÀ ĐÁP ÁN THI HSG TỈNH MÔN TOÁN - Pdf 17

 
  !"
#$ 

%&'(')*+,


( )
( )
 
 
 
    
y x x
x y x xy y

= + +


− + = + −


%&'('*+, 
 !
n
"#$%& '(
a
)

a n≤
*+,*-

$)
H
')@A*
ABC
-.=>
GH AN

%&0'(')*+, 
.=>

( )

B
B
   
4 54 54 5

a b c abc
a b b c c a a b b c c a
abc
+ + +
+ + + ≥
+ + + + + +
$%/
6 6 Ca b c >
%&)'('*+,
D&E$E1$FG*7H#%
C C×
4C!36C051I0 
!HE$IJC*,,7HK*),,*E0;,L*E

C-
• Q%
Cx =

 y x= − =
• Q%
x = −

 y x= − =
• Q%
x = −

 Vy x= − =
C-
X Y+
 y x= +
6*$),=61I
C6 6 Vx x x= = − =
C-
• Q%
Cx =

  y x= + =
• Q%
x = −

  y x= + = −
• Q%
Vx =


( ) ( ) ( ) ( ) ( )

B  
   N   C N   Ca a a n a a a a a a a− − ≤ < + ⇒ − + − < ⇒ − + − <
-QE'\4!,
Na

5-
C-
_,1"
a =
,L
Ba =
,L
a =
C-
X Y+
a =

{ }
 
 B 66B6666N6n n≤ < ⇒ ∈
C-
X Y+
Ba =

{ }
 
B  V66666n n≤ < ⇒ ∈
4!,

X c!d,=
BFEC
0+6*1I
GB GC GF GE× = ×
C-
X ^*
GF GE GM GA× = ×
C-
X _,1"6=
AMFE
0+-
C-
670
N
'/ 8
BC
4
H
'9 : 
ABC
&'(
')
;+<25 =>'6?6
GH AN⊥
X g,H+JO6$)=`hPi0+*
M
> 12312H#
AH
6
!,1"

X [1"
6 6M H N
9)- C-
X ,*
GAN
"*12*,
6AD NM
:*;
6H
 
H
')@AG**

GAN
-^*
GH AN⊥
C-
%&0'(')*+, '
N
D
K
M
G
F
E
H
O
B
C
A

B
   
4 5 4 5 4 5 

   
- - -  -

c a b a b c b c a abc
a b b c c a
abc
c a b a b c b c a abc
a b b c c a abc
c a b abc
 
+ + + + + + + + + ≥
 ÷
+ + +
 
 
≥ + + + + + +
 ÷
 ÷
+ + +
 
= + + +
_lmne*H$)MH

4 5 4 5 4 5  -c a b a b c b c a abc abc a b c+ = + = + = ⇔ = =
C-
C-


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