skkn giúp học sinh khắc phục một số khiếm khuyết khi giải phương trình vô tỷ thpt tô hiến thành
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (213.95 KB, 21 trang )
!
"#$%&'(
)#*"+,'%*
-.,/&$/"0*12'%34'
(56!"4#!7#,2"0"+$/"0
#8(9 :;<=!>?@A:"BC3#
*"BC32$/$/ :()#*#$%++
(9'';<D"B!E!FGD@'
:3'3.&#*H1I;J6#*!
D"B&C:?"0@KF8C3L&$/M
31N38+#*(
8#*$O%/$J'3.&D0!"
!P3 QL!$/@RS"C1C'8?$
2$(
M312C!#*0 CR"4T-
+U!"V=!3'#*(W-"4X
#*0+()#*Y0
#*ZTR"4[(
#*E)!I:"J>2$/\]!=$
A03D4#*L#*.U141L?^
8+12#8%TC(C-M3
8#*L#*.U141L?LV12(
>!&>2_9`_E9a=$O+"4
&#*!L#*bb+$/=3#
8*Cc"%%!0$$%!Dc
Z+$/$"T''*C(
deF>2$/"4\]J!T#*Yb"+I7
;%#f<(
deF>2$/"4\]DT#*Yb:L$#$
;%#fff("2deF
"01TCL!1IDTC^L2
3b12#8(aM3!:3 8g#
*L#*.U141L?c7$8Z,&
'3.!8'h?3 iTI(/DC!
3"CD-T '3"2812#*!
Z'ZIC,$"TZ8%$!^
$-12DJ!"S"C$'h?8
#*b6#UI(
<*L8,"B1-A-.g 4Q$
'3';
!"
e42-.%&;
_9$"T%$'8#*Y%C3"1'G
?3 ##%=c/$"T'8
\
#*Y.$/6UI(
_9'ZI,$"T$(
#$%$&
aIJE)2+12C%TC2+
%c(>/4TC!V$%/,'3.
!"'3.++""LT3(
//!=8Z,,.'
+/!3D1I"BC3+"2R
I:(>&: c7$81C
"$Ch"2(<*DC!*12C-T4
$-.+/!3D
1I"C3D!3J12D8+D4&
'(
#'(
j8#*L#*b$b0
#*>2$/\](C-!"01TCCL!$
'03D&12'(deF>2$/"4\]Jb
12#8;
! "=
!DdeF>2$/\]c*C'3.#8
#L&(C-!M3#L
12V(*"4\\\k!'8,
&#*b!$/$&"VV!8$D
'38(>!&>2_9`=$O#
*b&12'.'b6'' 12-!#
,/0$%T"M*C3&'3.(<*
DC!hV='h?/!^L-#
8#"LT36.T
M3C(+&L"*8
#-T8"B$$"TZ8
JC-J$"T:=:$J#60+8/
$C(
a+1%$'3'C/Z*Cl!'
!"m04E)"Dc&''?14C: R
E)4L"0T%$'(>&0$n
1I:812CQ1o=$'/\]E)D
=$"4\kU'p/E)!9
`>(I%&'B-L8#8
#*Y%C3b,$"T%$'8
#*Y#;j3 ##UI(9TC
$:$n1I&C"/:
8C3DI:(dq1I!8&,DgP*"D
'ZI,$"T#8V$:*,#
8/L!:0,"8$$%L(
k
)
*+, /01234567,-8639:,;,-<67/34567,-8639=>?@AB163C9D@/E/F<G@
23B<67,-863H3E/
)#*Y"++D#*12C
4h"#*U$/6141L?(
aCR"4[$ZT"=,8#*C&
D(
W-"4\]$0#*.U?D"0
L(CJ/#*^A$
P3 :8#*Y"#$:8#*Y.
2#"#*Y$-(
F8#*Y8MP3 :?.'n
:&#*A38!1D34L&
"2#*I:"(
_ )#*.U141LC/(
_ )#*D
_ )#*D
_ )#*"0
_ )#*^"
'8#*Y!&$J0'"
3 ##!'"3 81N4gL2
"(
>/4#*U141L?Dr!'J"^CRDr
3/##*38'J(s'8bT
':&''8n"2#*T(
9c'J"-"^CRDr83'&''S*
"3 8-'8%#*/8n"2/4
#*T(
>/4#*.?D"t'J"-"^CRD"t"0
#*##
IE/J1@FK>,34L677M2/013N/J@63H3@7@O@234567,-8639:,;9=P@C623E2
H3Q/23R/
*8#*$"T$Z8"$n
1IP3 '##1N4"+i&g
%#*1N4&'g:"
L-(
F8#*Y$Z,$"T$(
S1@FK>H3@7@O@234567,-8639:,;PT67/E/P@U6VW@,4567
V4567
SS1@FK>H3@7@O@V@XBH@C6YE/V+63
9,8#*Y"8%6T
*&'g(ah"!*V&'g*1u*
LC"!D&'gb"+(bTC
C#*A"C'38%(CDC*&
v
'g1N48+L#*!1uJCT"N
$
.ZRSe8#*
k
\ \ \$ $ $− − + = +
H\K
9$8$;
>F;
k
H \KH \K ] \ ]
\ ]
\ ] \ ]
\ ]
\
\
\
$ $ $
$
$ $
$
$
$
$
+ − ≥ − ≥
− ≥
⇔ ⇔
+ ≥ + ≥
+ ≥
≥
⇔ ⇔ ≥
≥ −
FH\K
H \KH \K \ \$ $ $ $⇔ + − − + = +
s
\$ ≥
-3
\$ +
\ \ \$ $− − = +
<4
\$ ≥
\ \ \ \ \$ $ $ $− < + ⇒ − − < +
1 # * A
(
1@FK>[V\]F=Z<
^=%$TLE)Nc8J
+:.JnQJ0:gP1LJn
=!':"LE9d(d1hLE9d8"DC*=0
"B&1L%.D(
wd'J:.TJn!+4'3.&3
##c/!=1uZ$"T$
] ]
] ]
!" !
! "
≥ ≥
⇔
≥ ≥
I@C623E2H3Q/23R/J1@FK>634,-_6
^e-C-T$4;
]
A
]
]
]
]
!
"
!"
!
!
"
=
≥
⇔
≥
>
≥
!#M
]
A
]
]
]
]
!
"
!"
!
!
"
=
≤
⇔
≥
>
≤
(
wCDC&R-"&'3.!c'M-12C
$8&'"+L#*D+!1u"6
>"B&1L%.D.'J+.D
.DL"8$-(e-"B-$;d
'8:&'g*-1M&'g:J
06gP1L&.14?DH+?DrK!'
:VVk3#*!3%#*@
W8V(
>F;
k
\
\
\ ]
\
\
\ ]
\
$
$
$
$
$
$
$
≥
≥
− ≥
⇔ ⇔
≤ −
= −
+ ≥
≥ −
x
LCgy_\V#*A(
H\K
H \KH \K \ \$ $ $ $⇔ + − − + = +
a3
\$ ≥
-3
\$ +
\ \ \$ $− − = +
<4
\$ ≥
\ \ \ \ \$ $ $ $− < + ⇒ − − < +
! 1 # * A
0C(
<DC#*Agy_\
CDC!'*&'+#*Y31N488+
L#*DvHD#K*&''7"8J
&.-3Jn(dO'L&*3Jn&"
.DL4"^CRD"tH"D\K!CDC3&.
gLJn".DL4$/^rH"DkK*$
"21uZ$"T(
.ZR`
v
v k \ k$ $ $− + − + + =
E$"$
>&':?.h;
v v k
v k ] v k ] H \K H kK ]
\ ] \ \
k ] k
\ \
$ $ $ $ $ $
$ $ $
$ $
$ $
− + − ≥ − + ≤ − + ≤
⇔ ⇔
+ ≥ ≥ − ≥ −
+ ≤ ≤ −
⇔ ⇔
≥ − ≥ −
<DC'Q2%g:?.Qh-#
*(
9:b4gy\*8?.&hgy\"
%#*(E$A$'8L#*
k
H \K H kK ] k ]$ $ $− + ≤ ⇔ + ≤
I@C623E2H3Q/23R/
wE$"MC3*LCT6;
k
]!! ! %> ∀ ∈
!*"O
-'+3Jn12
k
!
=CV+3$.
JC#70
]!
=
(s'+Jn"
k
!
6+3
%L#*8:*&'g*-T
$J"0;
]!
=
k
] ]! !≠ ⇒ >
!:R*0&'g/4Jnc
"2(
W8V;
>&':?.h;
v v k
v k ] v k ] H \K H kK ]
\ ] \ \
\
\
k
\
$ $ $ $ $ $
$ $ $
$
$
$
$
− + − ≥ − + ≤ − + ≤
⇔ ⇔
+ ≥ ≥ − ≥ −
=
⇔ ⇔ =
≤ −
≥ −
ngy\#*
k k=
-gy\"1CL(
z
{1I-LC8&'g^TQh4
8L#*(<*DC,12':C8V&'g
h""0(3IgCL&-!-"B-
$;a3&'-71Ly!0L#*;
k
]! " >
*
*'4|
jJC*$$O:6;a3
]! =
*L#*C!3
k
] ]! !≠ ⇒ >
!L#*;
]" >
S`1@FK>H3@VM,V@XBH@C6VaP@U6VW@234567,-863
11@FK>H3@7@O@234567,-863ZG67
H K H K& $ $=
'8#*
H K H K& $ $=
$3 $;
k
H K H K H K H K& $ $ & $ $= ⇔ =
!oT#+V*
k
H K ]
H K H K
H K H K
& $
& $ $
& $ $
≥
= ⇔
=
d'80$'n"2#*T
'`C"%#*Ab':&
'
H K ]& $ ≥
'3"D"%#*T(
.ZRbe8#*;
k$ $= +
E$'3.C3"$;
k k
\
k k k ]
k
$
$ $ $ $ $ $
$
= −
= + ⇔ = + ⇔ − − = ⇔
=
<DC#*Ak";gy_\gyk(
+$/$'*406;>:?.Dh*&
.6141L?D8'J!1=C"$;
k k
k ] k
k
k k ]
k
\
\
k
k
$ $
$ $
$ $ $ $
$
$
$
$
$
+ ≥ ≥ −
= + ⇔ ⇔
= + − + =
≥ −
= −
⇔ ⇔
= −
=
=
<DC#*Ak";gy_\gyk(
I@C623E2H3Q/23R/J1@FK>,-_6
>:'ZI$"T-$!41N$8=#
$
k
k
H K ]
H K H K
H K H K
$
& $ $
& $ $
≥
= ⇔
=
e-"B$"&'
k
H K H K H K ]
& $ $ & $= ⇒ ≥
-&'g
07A(<*DC-L2$;F12-
'T*&'g%#*bTJ3&
'%#*H
H K ] $ ≥
K
W8V;
}
k k
] ]
k
k k ]
]
k
\
k
$ $
$ $
$ $ $ $
$
$
$
$
≥ ≥
= + ⇔ ⇔
= + − + =
≥
⇔ ⇔ =
= −
=
<DC#*Agyk(
P1@FK>H3@7@O@234567,-8639:,;/3c1/d6Pe/Ff
98#*Y.?D"t%C31412?
Dv(
>/4$C3!*;e-"B$:.
h&Q2?D"t!46'0T"N+&':
.6141L?D"t8'J(
9"O#*.?D"t3 Q
0&#*12
v v v
H K H K H K H\K& $ $ $+ =
!#*C$
3 $
v v v
v
H\K H K H K v H K H KH H K H KK H K& $ $ & $ $ & $ $ $⇔ + + + =
HkK
d'8g#*HkK$'3"D"%HkK"
%H\K(
E/J1@FK>>Q/23O@
^E$"?D"t*'&'g&
.2?Dr!D&'g"g
%∈
-.8
3 !C3$O0#*##4#*
T(
w{12-$"T%$"6H\KHkK"#
*##M#*'##*AC
3
v
H K $
v v
H K H K& $ $+
(
I@C623E2H3Q/23R/
M3LCC8$'^:Z8$"TC(s
:'ZI$"T$!-L26H\KHkK'#
##*HkKb"#*8%#*H\K-'8
g8n"2#*H\K(
.ZRge8#*;
v v v
\ k \ v \ H\K$ $ $− + − = +
W8V$;
v v
v
H\K \ k \ v H \KHk \KH \ k \K v \$ $ $ $ $ $ $⇔ − + − + − − − + − = +
v
v k k
v H \KHk \KHv \K v
]
} ~ ] H} ~K ]
~
}
$ $ $
$
$ $ $ $
$
⇒ − − + =
=
⇔ − = ⇔ − = ⇔
=
n"2H\Kbgy
~
}
"7A(<DC#*gy
~
}
(
~
•l63$"TA-*$O1N4"LC-
2"gy]
/1@FK>H3@7@O@234567,-863/3c163@XB/d6Pe/31@
F8#*.&?D?#3 #
#!DLC6;{#*12;
H K H K H K& $ $ $+ =
!$
T"N!'C1Lw1L_!."#*12
H K H K H K H\K& $ $ $− =
!$Z$"T(
E$3 $
k
H K ]
H\K H K ]
H H K H KK H K
& $
$
& $ $ $
≥
⇔ ≥
− =
j3 -$^A:+T:3%*H
1mc$K(E$&'/4
H K! H K& $ $
'&'/4
H K $
*6!$O8*#k3%#*:'n?D!&
1N4
k
H H K H KK H K H K ]& $ $ $ $− = ⇒ ≥
!$ChC^::'=
0!"O= A+ T1I"/1C'8 #*12
H K H K& $ $=
H6#*#3K(gP+1II:;
.ZRhe8#*
v \ k \$ $ $− + = −
W8$%$;
k
k k k
]
v \ k \H\K v \ ]
H v \K k \
]
]
\
v
\ Hv \K
x \ k Hv \K k \
] ]
\ ] \
k \ v k \ ]
]
\
\
\
k
$
$ $ $ $
$ $ $
$
$
$
$ $ $
$ $ $ $
$ $
$ $
$ $ $ $ $ $
$
$
$
$
≥
− + = − ⇔ + ≥
− + = −
≥
≥
⇔ ≥ − ⇔
+ = +
+ − + = −
≥ ≥
⇔ + ≥ ⇔ ≥ −
+ + = + − − =
≥
=
⇔ ⇔ =
= −
<DC#*A;gy\
9:LCCgy\'8"%#*(
N/J@636=]23G>63i67J1@FK>J1B
X
d1h=$Cbk&'
]$ ≥
!vgw\
≥
]*6
k
k \ H v \K$ $ $− = − +
$O1N4kg_\'J!-'T&'kg_\
≥
]
,(D3-&'kg_\
≥
]*N$*&'C'304
k&'-$O;g
≥
\
k
!&'C1N4'"20gy\(
d"T6q3k3m1LC'A*#!I
:"30cA&'g
≥
\
k
*38'J!c
v \$ $− +
*
g1L(
I@C623E2H3Q/23R/
>:'ZI$"T$TL2/*#3
:0+#*##*k38m1LHML
""3'JK(41N$3 $;
H K H K H K H K H K H K& $ $ $ & $ $ $− = ⇔ = +
k
H K ]
H K ]
H K H H K H KK
$
$
& $ $ $
≥
⇔ ≥
= +
a&$'3.C3cZ8$"TJC#
H K H K H K H K H K H K& $ $ $ & $ $ $= + ⇔ = +
aDC!b6+C:3 1L!-AT:
'ZI0$"TL-$(
W8V-;
k
k
k
v \ k \ v \ k \
k \ ]
v \ ]
H v \ k \K
\
k
\
\
k
v
} \ k H€K
z k } \
$ $ $ $ $ $
$
$
$ $ $
$
$
$
$ $ $
$ $ $ $
− + = − ⇔ = + + −
− ≥
⇔ + ≥
= + + −
≥
≥
⇔⇔ ≥ − ⇔
− − = −
= + − −
aDLC4
\
k
$ ≥
*38%H€K'J!c3%H€KJ!1H€K
C#*A
Z1@FK>H3@-j,7N63<M/23\6,./363\6,k/l/3c1/d6Pe/31@
E$LCT"N'+#*Y.:.
1412;
• •
! !
" !"
" "
.ZRme8#*;
[
k
H zK k
z
$
$ $
$
−
+ = +
+
E$Z$"T$;
k
k k
k ]
k
H zK k H zKH kK k
z
H zKH kK H kK
k
k
\x
v \] x x
$
$
$ $ $ $ $
$
$ $ $
$
$
$
$ $ $ $
+ ≥
−
+ = + ⇔ + − = + ⇔
+
+ − = +
≥ −
≥ −
⇔ ⇔
= −
+ − = + +
<DC#*A
LC6'Cgy_\x#*ALC7A#
*(sgy_\x8"%#*A(
<DCC-J1N4"8-$|
E$$"T'6
!
" !"
"
=
!$"TC1':B*31L%
:.!"
I@C623E2H3Q/23R/
we-T"B$6;
]! ]
]! ]
!" ' ! "
!
"
"
!" ' ! "
≥ >
=
− < <
e-b$LC6"8-3+0‚ƒ]•jƒ]
-1N4Lgy_\x
wF12C88&'g
]
!
"
≥
!Q1M&'
gP1L%&.
!! "
:J0g!1N4V:
.V(
W8V;
>F;
k
k
]
z
z
$
$
$
$
≥
−
≥ ⇔
< −
+
a3
k$ ≥
!;
k
k k
k ]
k
H zK k H zKH kK k
z
H zKH kK H kK
k
k
\x
v \] x x
$
$
$ $ $ $ $
$
$ $ $
$
$
$
$ $ $ $
+ ≥
−
+ = + ⇔ + − = + ⇔
+
+ − = +
≥ −
≥ −
⇔ ⇔
= −
+ − = + +
)#*0C(
a3
z$ < −
!;
k
k k
k ]
k
H zK k H zKH kK k
z
H zKH kK H kK
k
k
\xH Agƒ_zK
\x
v \] x x
$
$
$ $ $ $ $
$
$ $ $
$
$
$
$
$ $ $ $
+ ≤
−
+ = + ⇔ − + − = + ⇔
+
+ − = +
≤ −
≤ −
⇔ ⇔ ⇔ = −
= −
+ − = + +
<DC#*Agy_\x(
\]
.ZRne8#*;
(kKkHK\H
k
$$$$$ =++−
E$"$;
)
\ k k \ k k$ $ $ $ $ $ $ $ $⇔ − + + = ⇔ − + + =
H€K
9?.h'
\$ ≥
!'
H€K
k
k k k \$ $ $⇔ + − = −
k k
[
x x X x x \H \K
X
$ $ $ $ () $ $⇔ + − = − + ≥ ⇔ =
*+
<DC#*A
[
X
$ =
,
aDLCCgy]^"+%#*
F3 -!$Z$"T'6
(!" ! "=
>`
.CbV'
! ]! " ≥
(a3
! ]! " ≤
*
( (!" ! "= − −
I@C623E2H3Q/23R/
we-T"B$6;
]! ]
]! ]
! " ' ! "
!"
! " ' ! "
≥ ≥
=
− − ≤ ≤
wF12C88&'g
]!"
≥
!Q1M&'
gP1L%&.
!! "
:J0g!1N4V:
.V(
W8V;
>F;
H€K
]
\
k
=
≥
−≤
$
$
$
(
€gy]"+%#*(
€
\kkkkk\\
k
−=−+⇔=++−⇔⇒≥ $$$$$$$
X
[
\xxXxx
kk
=⇔+−=−+⇔ $$$$$
HDK
€
KKHHkKkHK\Hk $$$$$$$ −−=−−−+−−⇔⇒−≤
X
[
\kkkkk\
k
=⇔+−=−+⇔−=−−+−⇔ $$$$$$$
H"2K
<DC%#*A";gy]gy
X
[
j-c8$;
\\
>F;
H€K
]
\
k
=
≥
−≤
$
$
$
(
)
K\kHKkHkxKkKH\Hkk
kkkkk
−=−+⇔=+−++⇔ $$$$$$$$$$$
kkkk
K\kHKkHx −=−+⇔ $$$$$
H1'H€KK
( )
=
=
⇔=−⇔
X
[
]
][X
k
$
$
$$
H7H€KK(
o1@FK>H3@PpV@P@aB,3c/634631B[31@9U/01234567,-863>=H3:67Vaq
V@XBH@C6
F3 +#*Y312
! " ! -+ = +
!$
Z$"T";73:.
!
':B3&'
%(
.ZRre8#*;
k x \ k v x \}$ $ $ $− + − = − + −
E$Z$"T$;
k x \ k v x \} k x \ k v xH xK
\ ] \
\ k v k
\ k v k
$ $ $ $ $ $ $ $
$ $
$ $ $
$ $ $
− + − = − + − ⇔ − + − = − + −
− ≥ ≥
⇔ − = − ⇔ ⇔ ⇔ =
− = − =
<DC#*Agyk(
aDLCCgyk'8"%#*A(
I@C623E2H3Q/23R/
e-"B$6;
wF7:."2n/3*8&'
w9I:"B;
]!
! " ! -
" -
≥
+ = + ⇔
=
W8V;
k x \ k v x \} k x \ k v xH xK
x
x ]
x
\ ]
k
\ k v
\ k v
$ $ $ $ $ $ $ $
$
$
$
$ $
$
$ $
$ $
− + − = − + − ⇔ − + − = − + −
≥
− ≥
≥
⇔ ⇔ − ≥ ⇔ ⇔ ∈∅
=
− = −
− = −
<DC#*A
\k
`1@FK>H3@7@O@P=@,<E6/l/3c1,31>J?PT6723456723E2
VM,s623R
`S1@FK>H3@H3:67VM,V@XBH@C6/3<s623R
.ZRt*:#*$
k \. $ $− = +
H\K
e8;
>y
\$ +
k
\$ ⇒ = −
H\K
k k
\ k k \ ] HkK. .⇔ − + = ⇔ + − − =
E $ Z $ "T; )# * H\K
⇔
HkK
\ \ ] k. .
′
⇔ ∆ = + + ≥ ⇔ ≥ −
(
E$CZ8$"TC"1L0"4"4[;>:+#*
Dk*&'"
]∆ ≥
(<+1I'`C'
:6&bV''&'+(
I@C623E2H3Q/23R/
wFUI8&'%UI
ws2-86#QHMLbT"D8
3-%$/DK
w<*:$/$+3+'#8-$"4\k:
"=#$/(
W8V;
9\;9$"4\](
)#*H\K
⇔
HkK
] ≥
⇔
`Cyw\ZQC
y
k
k +
2,:+'J
\ ] \. .
⇒ + ≥ ⇔ ≥ −
9k;9$A'3."4\k(
k \ k \. $ $ $ $ .− = + ⇔ + + =
„P$/
[
H K k \! \• K& $ $ $ $= + + ∈ − +∞
()#*A'Q
$/Cy…HgK`Cy:-
†\• K+∞
;
\
H K \ ]! H\• K
\
& $ $
$
′
= + > ∀ ∈ +∞
+
s$/
H K k \& $ $ $= + +
Q3-
[
\• K− +∞
!1
H K H \K \& $ &≥ − = −
(
<DC#*A'
\.
≥ −
``1@FK>H3@VM,V@XBH@C6/3<s623R/3413<=6,<=6/3.63YE/
-M3$8+$"T,";9&'UI
4"&'T.8&'%(
.ZRSu*:#*$;
k k
k k \ ]$ $ $ $ .− + − + − =
H\K
e8;
>;
k
k ]$ $ − = ≥
!H\K
k
\ HkK .⇔ + = −
E$Z$"T;)#*H\K
⇔
HkK
] ≥
E$Z8$"TC"1T6bT
] ≥
"%M
] ≥
4b"&'T(
\v
8*&'%%(
;>F;
k
k ] ] k$ $ $− ≥ ⇔ ≤ ≤
!'
k
k
k Hk K \ †]•\‡
k
$ $
$ $ $ $
+ −
= − = − ≤ = ⇒ ∈
<DC#*H\K
⇔
HkK
†]•\‡ ∈
⇔
`Cy\_ZQ
Cy
k
+
2,:++†]•\‡
R 8 3 - LC C- T % 0 7 A
] \ k \ \. .
⇔ ≤ − ≤ ⇔ − ≤ ≤
(
I@C623E2H3Q/23R/
e-"B$;F8+#*YH+
#*L'pK6#UI'.$/*:
&'TgH'UI.?D$
+&'UI'J=+=K'83
"8(aC-J"*4*0'7A&'T
g-*88+#*,!#*C$OV*
0%#*T(
C-#*.$/!3&''
g$O1N4"8$(aC-J"*'*C
'38!Q83+#*,'.$/(
3I"B-$;{,:$/-
+3-*:"6#$/!':bU
J3&'g%#*H3N"$/43
TK!0,$$''3&'g
UI
9k-;
k k
H\K k k \$ $ $ $ .⇔ − − − − =
„P$/
[
k k
H K k k \! ]•k‡& $ $ $ $ $ $= − − − + ∈
;
k k
\ \
H K k k H \KH\ K
k k
$
& $ $ $
$ $ $ $
−
′
= − + = − +
− −
)#*A
⇔
Q$/Cy…HgK`Cy:
-†]•k‡
_
∞
\
k
−
]\w
∞
k
+
\x
]
k
g _
∞
]\kw
∞
H K& $
′
]
&*$+
R83-LC#*A'
\ \.
− ≤ ≤
`b1@FK>H3@Fv]7@E,-+/3M6Z4D@w3<M//3M6,-_6x/01,e27@E,-+F=7@E,-+63p
63v,w3<M/FD663v,x/013=>J?
'86#2$CZ$"T"
"LC14H-K%D"7LH"4LK
%$/(
.ZRSS*:#*$;
z$ $ .− − =
@O@
>F;
]
z
z ]
$
$
$
≥
⇔ ≥
− ≥
„P$/
…HgKy
z$ $− −
!-
†z• K+∞
\ \
H K
k k z
z
]! z
k H zK
& $
$ $
$ $
$
$ $
′
= −
−
− −
= < ∀ >
−
83-
_
∞
zw
∞
H K& $
′
_
H K& $
\z
z
]
]
\
\
_\
ˆ
w
E$'3"D#*'
] z.≤ ≤
!$"TZ
8"1$"T]"7L%$/…!ML"
14(
F3"DV;)#*'
] z.< ≤
`g1@FK>H3@VE637@EJ1@9X>?@AB163C,4567c677@i1s6/y9=s6>D@
.ZRS`9#*;
(K}KHvH}v $$.$$ −++=−++
*
.
:#*AV+(
E$"$;
>F;
v }$
− ≤ ≤
>;
k[}v
k
+=⇒−++= $$
K}KHvH $$ −+
H€K(
‰1Ij>9$;
[K}KHvHk ≤−+ $$
-RH€K
(kvv ≤≤⇒
)#*A;
.
. k[k
k
[
k
k
−=−−⇔
−
+=
K\H
)#*AV+
K\H⇔
V+
‡kv•v†∈
⇔
Q
$/
[kKH
k
−−= &
`
k .= −
b+:-
†v•v k‡
(
_
∞
\v
v k
w
∞
k
k [ − +
sM83-LCQ$/
[kKH
k
−−= &
`
k .= −
b+:-
†v•v k‡
} k [
} k [ } k v
k
. .
−
⇔ − ≤ − ≤ − ⇔ ≤ ≤
(
su1LCC'yv#*Ak";gy_vgy}!
DC"8-"$(
<DCC-J$"T6q|
E$A$'6;)#*AV+
K\H⇔
V+
‡kv•v†∈
(RD&C."$A$M
#.\_\,U^
† }•v‡$∈ −
U4
†v•v k‡ ∈
(5C$q;
+
† v•}‡$∈ −
$O+
†v•v k‡ ∈
+
†v•v k‡ ∈
4*:&
† }•v‡$∈ −
.'8b"+Hh"
\}
_}
[ } k−
k
4
v } $ $= + + −
*l"+$/%/$/gg'8"
$/%/$/K
I@C623E2H3Q/23R/J1@FK>/3<3N/J@63
9/-!/4q-V'"2*12C!
08+ 36#ŠŠ>&'9T%‹‹(g
'*C"CJC/*C":$$7$
"T3$n,(
;
} v v
• ] } v
k
k H} KHv K
$ $
$ $ $
$ $
− − +
′ ′
= > ⇔ − > + ⇔ <
− +
g
_
∞
_v
v
k
}w
∞
′
w]_
H K& $
<DC;
† v•}‡$∈ −
#.
†v•v k‡ ∈
!CDCC'8"
#.\_\(LC:b+%
† v•}‡$∈ −
*
v k =
!'
v
k
$ =
(H
†v•v kK∀ ∈
&k
† v•}‡$∈ −
K
s#*AV+
H\K⇔
v k =
'
†v•v kK ∈
(
<4
v k =
!y
} k [
k
−
(
<4y
} k [
k
−
!#*
k k
v kH ΠK
} k [
k [ kH K k \X } k ]
k
k v kH"K
.
=
−
− − = − ⇔ − − + = ⇔
= −
sM83-%$//*$K-LCC
v k = ⇔
v
k
$ =
<DC;
} k [
k
.
−
=
"T*(
51I-LC6T8S"C-$*D
Ug#&$M#.\_\!'8:J"+$/(
a,1I':-$OV$C?"M1C!+?
\~
v
v
v k
v
"MTgC-Q1o*12C$/!^12C8
#*!L#*(
l>FG@F8#*Y!4/0$*&':
CC-T#;j3 ##UI(e
-T41N$J0C(
>:V$'ZI,'3'C3'8#*Y
6#3 ##*-T8'Z$J$
0,P3 ##$JC;
€0+?
k
k
k \
k \
k k
k \ k \
k
H K ]
H K H K
H K H K
H K H K H K H K
H K ]
H K H K
H K H K
H K H K H K H K
H K H K
$
& $ $
& $ $
& $ $ & $ $
& $
& $ $
& $ $
& $ $ & $ $
& $ & $
+
+
+ +
≥
= ⇔
=
= ⇔ =
≥
= ⇔
=
= ⇔ =
=
€0#*&?Dr*-12C$3
C:3 1L1N4k3'J!R&'0:*
#3'n1L?(
€0#*&?D"t*3"^CR3:'n?
$n1IPC361I83&*$'8g
8C#*T:"22"(
€e-^T38$,'3.:8L
#*#86II*V&'%L#*
Y(
€FV+:.Jn.?Dr-$
4'h"";sM&'g%#*:J
0+g1N484:.+VZ(F
84+2n.?Dr3*8:B3&'%
(
>:V$'ZI'3'C3'8#*6#
UIT"B$$;
€>/4#*'.$/*:bT&'T
g"8NV(CDC3=0&'g
*$O1N4"8i#!488,#*(
€F8+#*YH+#*L'pK6#
UI.$/!3&''g$O1N4"
8$(aC-J"*'*C'38!Q83+#
*,'.$/(e-3I"B-
$;{,:$/-+3*:"6#
$/!':bUJ3&'g%#*
H3N"$/43TK!0,$$''3
\X
&'gUI(9c3"$/43$/"UI*
8&'g4"8V(
€e-12C$3*/#.,U^U4
:0"8gL(e-"B$;F8'
,U^U4^"\_\(
€e-TU/$'3.&42$/:="D
V83-(WB$'0T,"4LH7LK
442%$/(
$&
)#*b+8'3.#/'/4$"4\]
-DE)"2&':!&'8
$L"08&>2_9`(<*DC!JC"T0&TC
$J(*12C$"4\]D$
"4\kTC!1#/&:S"C$
'G?8#*Y%C36##8;j3 #
#UI!$qV,DgP!VB
:=-'3D1I:8D#M!
,$"T(•-/4$"4\k!3I2
/"2=12#*b(a!
=R4"=4&#*b&>2
9`(<4"DC!$/$"4\]$"4\kA
0'h?88D&TC/#!3D12^3
+#*b&12=+A380,
$"T'(
F38I:"4'/\]!$'1I$'3'C
812C0:':n$;
a? W4 $/
>:X"- >:Rz3X >:14z
d/
"0
Y"
d/
"0
Y"
d/
"0
Y"
k]\k_
k]\v
\]9\ xz ~ \X• k] zv• \\ k[•
\]9k v} z \x• \~ x~• \x v[•
aDCLC$'3'-8#/(1m/Z
*c!-.$ZZc&3$23(L
0$MJ%L8Q $B(gJ
8#(
z
a6V$/#T#*b!8J'3;
_J/#*"4\]!LUC&-?
-$/3+1C(
_>/4$"4\k!--1+$/3$:D"2
=#8#*b#8^L-
\[
=$'!7+$/DJ6U/=
'*>29`(
„‰9aEŽa
9•‚E•••{ae>‘a<’
01234.5678
gJC"dFFa%*
3!'$P+1%
'(
W-a)#
k]
{$|*}
\K d'>2$/\]#8J_9$:;3)<=(
kK j t_9$:;3)<=(
vK 9&>2_9`?(
xK J>2$/"4\]_)ECF8_9$:;3)<=,
k\
