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PHẦN I: MỞ ĐẦU
I. LÝ DO CHỌN ĐỀ TÀI

 !"#$%&'(")"
**%+",-*./01+$23"'4
(5*6723"832
292822"*0:822
 ;<""=2#>$?
,*@0A$$;"=B+2'
2822$(/*B0A(;
C&"-*4D4(/$E"92
8*0
II. MỤC ĐÍCH NGHIÊN CỨU
AFGH%F8I>J3H$2I
AK:A%LB"3H$0A(;MN2%
BOHDP8*"*0
 Q=H@$(""R2"=
2822B/3%3"*>N2@*
*0K$.$92*SB2L
<""=&HBT28223"=2
*"*0
III. ĐỐI TƯỢNG NGHIÊN CỨU
7N?*!*+*4
!*+NHM@$**&28)
3'@**'MNM@$**&280
IV. PHẠM VI NGHIÊN CỨU
 U=H2#*8&VW*
7XY0
V. PHƯƠNG PHÁP NGHIÊN CỨU
Phương pháp:
U?G+%3F>'H$%M


N2%99B"0
Z)2*"*"*4H!N
*4HJHHM@*&28
%0000%
[[[[
qpnm ++
A'+2
<8=,N2?B=\<<]5$=H
<88*E
%0000%
[[[[
qpnm ++
2HD*?
4''/3*0
Cách thực hiện:
AMSB2%"3G'?L*="(0^?
B>'%2HD99B"//&3
H$0
A(/B3H$>'2I2VWV[!"
#$0
VI. NHIỆM VỤ VÀ YÊU CẦU CỦA ĐỀ TÀI
 _2FGH%'B">BB"
D`a92?>BB"DNHD%
92&H$b!2,4'"=
39,N2)2*"*0c+$
?23*'+H2*BN
?OHD=@P8B30
 d?#@'B"`U=H322e(
"(,2LN2%M"0aBN
H8*3%OHDN2,=P83F*D40

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 7N(>'23H$>*&
*&?2#*N2%&$
(*'*C#F**0
QB34"hqB+2%"*+2$
+$*./)(3N0
III. GIẢI PHÁP TỔ CHỨC THỰC HIỆN
Q?M99B"F>'G'@
SB2("H3/$'?@
 322`7"=32292&r!
*'MOHDP8"*%*E28
222H2HD(80
1. DẠNG 1
\*OHD`A")2B=]5$
<8
nol
VV
yxa

%
nol
[[
yxb


(`
baba





00 ≤
$
[
[
[
[
[
V
[
V[V[V
0 yxyxyyxx ++≤+
%53$
%Vn%l baba




⇔=
L28
[
V
[
V
y
y
x
x
=⇒
0

A(B=]5$<8
nool
VVV
zyxa

%
nool
[[[
zyxb


  (  `
baba




00 ≤
 $ 
[
[
[
[
[
[
[
V
[
V
[

V[V[V[V
0 zyxzyxzzyyxx ++++≤++
% 
53$
%Vn%l baba




⇔=
L
[
V
[
V
[
V
z
z
y
y
x
x
==⇒
1.1 Ví dụ 1: Y5%$>.";mp5
[
sVp$
[
tu0Y"
E`

v
[w
w[
v
Vw
≤+−≤ xy
0
Li gii:
A$`mp5
[
sVp$
[
tlp5n
[
slv$n
[
$x[5t
xy p0
m
V
v0
v
V

0
A")2B=\<<]5$`








m
V
o
v
V
a


( )
xyb pov

$
v
w
mpVp
u
V
Vp
V
p0
m
V
v0
v
V
[
[[

=++≤−=− xyxyxy
i$#"0753$`





=

=







=
=









=
=+

[W
u
w
[
[W
u
w
[
m
V
p
v
V
v
uVpmp
[[
y
x
y
x
xy
yx
1.2 Ví dụ 2: Y5%$%ym>(".";
v=++ zyx
0Y
"E
[
Vzm
VvVmV[ ≤+++++ zyx
0

Li gii:\
v
V
v
m
V
m
[
V
[VvVmV[ +++++=+++++ xxxzyx
v
?(")2B=\<<]5$`
( )








+++
v
V
o
m
V
o
[
V

%vomo[ zyxba
`
[
Vzm
v
V
m
V
[
V
vm[
0VvVmV[VvVmV[0
=+++++++=
≤+++++=+++++=
zyx
bazyxzyxba
753$
0
VWz
[Vk
o
mp
vu
o
[k
Vk
v
V
v
V

m
V
m
V
[
V
[
V
v
===⇔











+=






+=







+
=++
zyx
zyx
zyx
1.3 Ví dụ 3: YmH85%$%y.";B5s$sytV0Y
"E`
0[
[[[[[[
≥+++++ xzzyyx
Li gii:
A")2")2B=\<<]5$`
nVoVln%oln%oln%ol nxzczybyxa



0A`
[[
0[0 yxyxan +≤+=

[[
0[0 zyzybn +≤+=


[[

0[0 xzxzcn +≤+=

i$`
0[nl[0
[
V
[[[[[[
=++≥+++++ zyxxzzyyx
753$`
m
V
=== zyx
0
1.4 Ví dụ 4: Y*>5%$%y.";B`



=++
=++
Vp
m
[[
[[
zyzy
yxyx
0
Y"`
z≤++ zxyzxy
0
Li gii:

U+$`
[[
[[[
[[
[[[
[[
m
[v
m
[[
m
[v
m






++








=







++=++






++








=






++=++
z

yz
z
yzzyzy
x
yx
x
yxyxyx
?*'M














++






+=++

[[
m
[[
m
m
[ x
yz
z
yxzxyzxy
0
A")2B=\<<]5$`








+








+ z
z

yb
x
yxa
[
m
o
[
%
[
o
[
m


i$
zVpm
m
[
[
m
[
0
[[
m
0
m
[
[
[[
[

==








+






+






++









≤++ z
z
y
x
yxzxyzxy
1.5 Ví dụ 5: Y%*%{W%{*{0Y"E
w
( ) ( )
abcbccac ≤−+−
0
Li gii:
A")2")2B=\<<]5$`
noln%ol cbcvccau −−
%`
( ) ( )
abvuvucbccac =≤=−+− 00
0
753$
cba
cb
c
c
ca VVV
=+⇔

=

0

2. DẠNG 2
\*OHD`A")2B=]5$
<8
nol
VV
yxa

%
nol
[[
yxb


nol
mm
yxc
(`

baba




+≥+
$
[
[V
[
[V
[

[
[
[
[
V
[
V
nlnl yyxxyxyx +++≥+++
%53$

ba%
L
[
V
[
V
y
y
x
x
=⇒
0

cbacbacba ++≥++≥++





$

[
m[V
[
m[V
[
m
[
m
[
[
[
[
[
V
[
V
nlnl yyyxxxyxyxyx +++++≥+++++
%53$

cba %%
("=L
m[Vm[V
```` yyyxxx =⇒
$
m
m
[
[
V
V

y
x
y
x
y
x
==
0
2.1 Ví dụ 1: YmH85%$%y.";B5s$sytV0Y
"E`
0[
[[[[[[
≥+++++ xzzyyx
Li gii:
A")2")2B=\<<]5$`
noln%oln%ol xzczybyxa



%`
( )
[[
[
[[[[[[
=++=++≥+++++=++ xyxcbaxzzyyxcba




753$

m
V
V
===⇔





==
=++
zyx
x
z
z
y
y
x
zyx
2.2 Ví dụ 2: Y5%$%y*H8 
V≤++ zyx
0Y"E
0z[
VVV
[
[
[
[
[
[

≥+++++
z
z
y
y
x
x
l,7Y|!"
[WWmn0
Li gii:
A")2")2B=\<<]5$`





















z
zc
y
yb
x
xa
V
o%
V
o%
V
o
%`
≥+++++=++
[
[
[
[
[
[
VVV
z
z
y
y
x
xcba
p
( ) ( ) ( )

( ) ( )
0z[zWu0VzzW
VVV
Vz
zW
VVV
zV
VVV
[
[
[
[
[
[
=−≥++−








++++≥
++−









+++++=








+++++=++
zyx
zyx
zyx
zyx
zyx
zyx
zyx
zyxcba
1+$*N"0753$
m
V
=== zyx
0
2.3 Ví dụ 3: Y5%$%y{W0Y"E
( )
zyxxzxzzyzxyxyx ++≥++++++++ m
[[[[[[

l,KBQBQ'%!"Vuukn
Li gii: N'
( )
zyxx
x
xz
z
yy
y
x ++≥








+






++









+






++








+






+ m
[
m

[[
m
[[
m
[
[
[
[
[
[
[
A")2")2B=\<<]5$`








+








+









+ x
x
zcz
z
yby
y
xa
[
m
o
[
%
[
m
o
[
%
[
m
o
[


( )
zyxcba
cbax
x
xz
z
yy
y
x
++=++
≤++=








+






++









+






++








+






+
m

[
m
[[
m
[[
m
[
[
[
[
[
[
[
753$
0
[
m
[
[
m
[
[
m
[
zyx
x
x
z
z
z

y
y
y
x
==⇔
+
=
+
=
+
2.4 Ví dụ 4: Y"E">
m
[
−≥x
`
0
m
wk
[[
[
m
v
[[
≥++++ xxx
Li gii:
A")2B=\<<]5$`
|lWo[n%lXVoXVn%cl5oWn
A`
%[[%v
[[

++=+= xxBMxAM
ac
V
4"5h*I`
BMMM
[
m
V
=
lH
m
[
−≥x
n







+
−⇒
[
m
o
[
m
V
x

M
%
$`






+
[
m
o
[
mm
V
x
MM

[[
[
m
[
V
++=⇒ xxMM









+

[
m
o
[
m
V
x
AM
%$`
m
wk
vunml
[
V
[[
[
m
v
[
VVV
[[
≥++==+≥+=++++ xAMMMAMMMAMxxx
k
753$}`
m

[
[
[
m
[
mm
m
[
−=⇔








=
+
−≥
x
x
x
x
0
2.5 Ví dụ 5: 1%*>L$G0Y"E`
Vm
Vw
vv
u

Vm
[
m
u
Vm
m
VW
[up[
[[
[[
≥+−++−++− a
aaab
bbb
0 lVn
Li gii:
A$`
( )
[
[[
mup[ −+=+− bbbb
%
( )
[
[
[
[
m
[
u
Vm

m
VW
[






−+−=+−
a
bab
aab
b
%
( )








+−=+−
[
[
[
m
[

[vv
u
Vm a
aa
a
A")2B=\<<]5$`|lWomn%l[oWn
( )
0o%
m
[
o bbN
a
aM






$`














−−−
m
[
o[%
m
[
on%mol
a
aBM
a
babMNbbAN
Z`
=AN
( )
[
[[
mup[ −+=+− bbbb
%
=MN
( )
[
[
[
[
m
[
u

Vm
m
VW
[






−+−=+−
a
bab
aab
b
=BM
( )








+−=+−
[
[
[
m

[
[vv
u
Vm a
aa
a
ac
V
4"5h*I
BMMM
[
m
V
−=

i$c
V
=Hh
28&[5xm$xutW0
aK&'(@|?H
( )
Vm
Vw
% ==⇒ dAdAH
%`
1+$*

lVnN
"0
753$|%U%c%c

V
%`
z
$
c
5
K
]
|
U
H
c
V

Vm
Vw
vv
u
Vm
u
Vm
m
VW
[up[
VV
[[
[[
V
=≥=++≥
+−++−++−=++

AHAMMMNMAN
a
aaab
bbbMMNMAN
\






m
[
o
a
aM
=|28&
Vm
Vz
Wp[m =⇒=−+ ayx
( )
bbN o
=|28&
w
p
Wp[m =⇒=−+ byx
A"53$
Vm
Vz
=a

%
w
p
=b
0
3. DẠNG 3
\*OHD`A")2B=]5$
<8
nol
VV
yxa

%
nol
[[
yxb

(`
baba


−≥+
$
[
[V
[
[V
[
[
[

[
[
V
[
V
nlnl yyxxyxyx −+−≥+++
H*E53$
a
L
ba −
 U'
( )
W
pW% =ba
&
baba


−≤+ [
$
[
[V
[
[V
[
[
[
[
[
V

[
V
nlnl[ yyxxyxyx −+−≤+++
53$
ba =
3.1 Ví dụ 1: Y[>2*B"0Y"E`
( )
( )
0[[[[
[
[
[[[[
nmnmnnxxmmxx −+−≥+−++−
Li gii:
A")2B=\<<]5$`
( ) ( )
0o%o nnxBmmxA −−
%
( )
( )
0%[[%[[
[
[
[[[[
nmnmOBOAABnnxxOBmmxxOA −+−=−=+−=+−=
( )
( )
[
[
[[[[

[[[[ nmnmOBOAOBOAnnxxmmxx −+−=−≥+=+−++−⇒
N"0
753$
0
mn
mnnm
x
mn
m
nm
mx


=⇔

=


3.2 Ví dụ 2: Y5%$>$M%Y"E
( ) ( )
m[[VV
[
[
[
[
+≥−+++++− yyxyx
%l,7%Y
!"[WWpn
Li gii:
A")2B=\<<]5$`

( ) ( )
yxbyxa oV%oV +−−
i$
( )
yba [o[ −−=−
0\
( ) ( )
=−≥+=++++− babayxyx
[
[
[
[
VV
⇒+
[
vv y

( ) ( )
[V[[VV
[[
[
[
[
−++≥−+++++− yyyyxyx
753$
W
[[
V
=⇔



=


x
y
yx
Z3"
( ) ( )
m[[V[
[
+≥⇒−++= yfyyyf
0753$
m~V%W == yx
0
u
3.3 Ví dụ 3: Y"`
( ) ( )
(
)
[[[[
[[
[
V
dcbadbca +++≥−+−
0A%
*%%HH8.";B`
m=
+


bdac
adbc
0
Li gii:
m=
+

bdac
adbc

m
0V
=
+


c
d
a
b
d
c
a
b
A")2B=\<<
]5$`|lo*n=O
x
a
b
y =

loHn=O
x
d
c
y =
%5{W0\
m=
+

bdac
adbc

?pW
W
`
[[[[
% dcOBbaOA +=+=

( ) ( )
[[
dbcaAB −+−=

\

( ) ( )
[[
[[[[
[[ dbcaBAOBOAOBOAdcba −+−==−≤+=+++
AF$*N"0753$
[[[[

dcbaOBOA +=+⇔=
4. DẠNG 4
\*OHD`A")2B=]5$
<8
nol
VV
yxa

%
nol
[[
yxb

(`
baba




−≥−
$
[
[
[
[
[
V
[
V
[

[V
[
[V
nlnl yxyxyyxx +−+≥−+−
H*E53$
% ba


L
[
V
[
V
y
y
x
x
=⇒
4.1 Ví dụ 1: C"E">5`
wVWpw[
[[
≤+−−+− xxxx
0
Li gii:
A`
VnmlVWp%vnVlw[
[[[[
+−=+−+−=+− xxxxxx
U?")2B=\<<]5$`
nVomln%[oVl −− xbxa



A`
wVvVWpw[
[[
=+=−≤+−−+−=− baxxxxba




0
753$`
0w
V
[
m
V
=⇔=


x
x
x
VW

|
x
b
a
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1. Kết luận
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2. Kiến nghị và đề xuất:

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(TG: Phan Đức Chính - Vũ Dương Thụy - Đào Tam - Lê Thống Nhất)
sAVWXPhan Huy Khi
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