NGHIÊN CỨU KHOA HỌC SƯ PHẠM ỨNG DỤNG ĐỀ TÀI: VẬN DỤNG HẰNG ĐẲNG THỨC ĐỂ RÚT GỌN BIỂU THỨC CHỨA CĂN THỨC BẬC HAI MÔN ĐẠI SỐ 9 TRƯỜNG THCS THỊ TRẤN TRẢNG BÀNG NHẰM NÂNG CAO CHẤT LƯỢNG MÔN TOÁN
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (708.25 KB, 58 trang )
!
"#$%&'&
(#)*+
$,-.
)/
012345675389!:;<:
/=>(?=@A
!"#
$%&'()*$+,*-
!"#$%&'&
(#)*+
$,-.)/
-
B3CD90 EF90
!"#$% &'!(#) *
+ ,(
/01$
234
56
* 7'8"#$ 3
2 79:%;$<$= 3*
4 $=%$>? 2
5 1$(%< 4
6 7@ !&,A)B-C# 53
7@@D.-E$-E(%E('0$- 3+
7@@@D.-%E($- +3*
7@F3G<-E(%E('0$-H 234
7$=IJKL-M% &H 5
+ 7$- N"#$% &'!(#) +6*6
G*H"IJ
KL3M4NOPNQ KL3M44R4
OP1P ON
D!&'!( DLQ7
DE($ DG
D1?$$R QS
+ D# DO
* /?$ /G
2 / " /F
4 L& LQ
5 E(
6 N"#$ NO
7'8)!>& 77SL
Q % Q/
T1( N
./012&3415 !"#$%&'
!"#
$%&'()*$+,*-
$ G
+ $&8U LOQ
I
!"#$%&'&
(#)*+
$,-.)/
N'V"#$WN$>XG:>
D8?W'VLOQ?YL$>1<G
1S7 TU4NB90
@V3894EU90 ;$<&='8@ ZD![05Y\&
'>=]&E$#,
#^#=\&-_.)Y$?
$>1-H
W0DPX995Y9
LQ %P & H LQ ? ` % # U 0
)'0H<^$KLQ' $H
/ "a &T(=
% ',1\',;$>H
T1=_:HL&_'V
&=H
?V3Z3[5\[45FP45M
678(9
*:;1
<=>?@%'AB
>V"]9N^9053X97_D
L'0)b&A)B-C#-E]&
E$##^= ()!>'8@
D!5,(9 Y'c(P %Pd
./012&3415 !"#$%&'
!"#
$%&'()*$+,*-
W3Z45DPM49053X97_D O,HL'0)b&A)B-C#-E]
&E$##^= ()!>
'8@D!5P;$1<=H
AV53M4`M %%E($--0,(b$
"\(,(T1(Z5e[(0-#
Z5e[HST %;$<%E(%< Y'c
-f$^((%E('0-%E(
'8@%E($-H
N,(
T
1(
Zg05
,
LQ[
h
S!>&,
'0)b&
A)
B-C#
-E]&E$
##^
=H
h
N,(-
#
Zg05
,
LQ[
h
S!>&%P
,A)
B-C#
-E]&E$
##^
=H
h
aVTb1290 QA)- %#\%i^;$%E(
H
T1%E(%< Y'c-f$^(
%E('8@ ,(WT1(-
#H
E(#-=>B'8j-=
./012&3415 !"#$%&'
!"#
$%&'()*$+,*-
(#-<'UH
cV5Y94d75Ceb38D :?-E($%E('0-
$-K,(T1(,(-#H
:"1-E($k,(-#
,(T1(-EI-?-"1H
:-1$RK%E('0-
$-K,(T1(,(-#
-E T9K-E(H
QA)J%E(#j-=(#-<
'UH
fVM4gDZ ;$<-01'0)b&A)B
-C#-E]&E$##^= (
)!>'8@D!5P;$1<=
&B(,f9 %;$<&=
D!05,li%Pd
N$,li(#-<'Um,f9
%;$<&= Z-![5H
./012&3415 !"#$%&'
+
!"#
$%&'()*$+,*-
@VhJ
n$Yk>"$f$.)$'8<)!>(P U
=LOQKG/SoD%c0p !"#qH
TX)!>&(P 5\P=Y>-E9 -'cY'c(P
( 1(k%#\ "_<T&
'8rc0\-'c&\sN'j P\(Y
#;$&k "< LQ-'c=)%#K&
<=.$ &(0t' $>1=LQ(0
,EE$9$(k%#-,=)-'c8H
u%P=Y>Bj(&\Y05<?$.$T
1A 'V$>"\'VP-E-?'0 '8K
($>HU%v-,\)$ 'V8 (f%#8
<%PE$-,'8^#= )'0)!]&E$#
T1J:^H7f0j(%P(-'c u(%P&w
=Kf>H
• !-1C)/
F.&W
O'(kB-C#-x-'c&U04H
y^=)B-C#-x&)'0)!E$##)Y$^U
05'! H
y^-z\: \< .^#=K-&_
>$H
F. "W
Y.$V\A)'81)!>&-E,E{$>1-'c%y
^=)B-C#-x&)'0)!E$##)Y$^U0
5t'%y^-z\: \< .^#= &H
D!-%A-A.-*?CEF@7;@C
F&'(kB-C#-x-'c&U04=)
B-C#-x&)'0)!E$##)Y$^U05'!
./012&3415 !"#$%&'
*
!"#
$%&'()*$+,*-
" "'V'0)b<HD9>'V#'0)b<
=E(%P,-?'0'8t'8U%#-'c
=) =HS -,&%P,%y^()b--&
:#]%< .^#=H
D.%A-A+'/
L'0)b&,%i^\'8< #^#=\
EWijCk905l90Nm9045_7En40o9p3qD45_77r75_F7s945_7pt75F3iV
F0T"PI-?('8"#$]&9
Y'c&=K&05e5e'VLOQ?YWWijCk90
5l90Nm9045_7En40o9p3qD45_77r75_F7s945_7pt75F3i,{$>1-'c%y
^&=K&H
N"#$-'c",(-'cb$"U05e5e
'VLOQ?YH
;$< Y>--x<'U|1-%;$<&=KLQ0T
1( 8 00-#W
}DE($K,(T1('0-05e+H
}DE($K,(-#'0-P05e+H*
};$<%E(#j'0-7~6\*5H
}DE($K,(T1(05e$-2H*
}DE($K,(-#05e$-+H2
};$<%E(#j$-7~6\6666H
?Vuv!
?V@V3894EU90!
N.$)!> "%PT1-'cj % !&'$R?
V+]HS ('c%#8.$\(
LQ$_=(\%<^: _%J(\ "(YV9$`\
=s
./012&3415 !"#$%&'
2
!"#
$%&'()*$+,*-
-,.$& "a -'c%#(0 LQ\_1
LQ-'c=)%# <=-E%9$%#_!\)b
-1(=.Kj('\=(:(j(_%P(-'c
H
'8 05\Q % 05=\=\-'
Y.$=.]&E$##^#=Y%,\,-_`&
<(kB-C#-x-'c&U04=)B-C#
-x&)'0)!E$##)Y$^U05-E-z]&H
D&05'VLOQ?Y',%y^(&>$
f>H•$%< T'0"#$\-f0 ")!>&
B'8$>.\G#6A<A-A?'67
8-(9E,?'*;H?'-
*?1IJIK+'')1$*
?@B
?V?V3Z3[5\[45FP45M!L'0)b&,%i^\'8< #
^#=\EWijCk905l90Nm9045_7En40o9p3qD45_77r75_F7s9
45_7pt75F3iV
?V>VB4wx9053X97_D0O9NYP!
}1$-z(077SL U'VLOQ$>" )!>&j '8
)!>&:TKf>N$>X•$L''VLOQ'8r•$9
}N"#$LQ7€S3G/SoDSTF13Ga !NOLQ7€S)
f>fD^O$>""QU/SoD9>NE%H
}Dz(0%E(%;$<&=&LOQ) f>7Lk$:O$>"
"QU/SoD9>NE%H
}L'0)bT1$R%#%i^(P LOQZG/SoD[H
?VAV"]9N^9053X97_D!
F1A)5l90Nm9045_7En40o9p3qD45_77r75_F7s945_7pt75F3
'8 05,{$>1-'c%i^\'8< #^#
= &05'VLOQ?Y<G>%Pd
?VaV3Z45DPM49053X97_D!
./012&3415 !"#$%&'
4
!"#
$%&'()*$+,*-
F1A)5l90Nm9045_7En40o9p3qD45_77r75_F7s945_7pt75F3
'8 05,{$>1-'c%i^\'8< #^#
= &05'VLOQ?Y<GH
>Vy/
D.L"8(9L
P-x"#$ ^(&66-x) <)!> "0H
;$"#$)\P-xA)'8%"\9 !
'8 %;$<T1(;$%E(K05e0
5e$G"!-,P-x \-$0'8<)!>Uk^(&
'0-E a >0( ($,E) <)!>
k^(&$H•$ >\PT? (.'8<)!>
-#>"$f$-z(0'8 )!>&1>H
>V@4-C/
N"#$-'c",(-'cb$"U05e5e
'VLOQ?YH
L0-'c&("#$b$"',.$-E('8
-M$W
}%&'()*WY<&0 $:T\K- &=\,l
# &=\?$%,$>i(_%(H
}%&+,()*-(W0'8-'8.Y'c
(P 4'V90 r(%%'8-'8$
.(u )H
g0 zLQ N( Nk S9%
5e 2
5e 4
>V?;I;C/
/ "WN$>XG:>,$z."6^(z'Uz -!
)1$i-$Ya.$^(.\ ^(&636=GB
%jKOK?€GNSa9>NH
./012&3415 !"#$%&'
5
!"#
$%&'()*$+,*-
O&05e0T1(ZN[,LQ\05e0-#ZDO[,
6LQH
G<W53M4`M9053X97_D
%%E('0$-0,(b$"W
5rz
3qz4EF
4E1S74\7
NB90
\7NB90
3qz4EF
wFD4\7
NB90
g05e
ZLQ[
h
S!>&,'0)bA)B
-C#-x&H
h
g05e
ZLQ[
h h
{3M95|95456790538z!
VT1(b$9j % !)!>&K
'Vj V%,E$-E-<(< :%;$\EW
52303F945675389
$f 77O ")!>
* g$>1=
2
•]&E$##^=
g$>1=
45 *2 ‚='8@
5 4 E('8@
>V>MNC/
"8U("$K )ƒ.!/.,01+!2!.34056
/7.+8- ! k 'VTK\^-\! \,^T<
;$>kY ) TX-u\-#>"$f$OP1 \1-!
-Y'0H$- ! -'c 'V% -V 'VTK\^-
! '8 )t<'0 1%8)=>\{$>1
E%<^i((TK\^-! > &=\
-U'VHF=>f<-z(0'8)!>&\)k
./012&3415 !"#$%&'
6
!"#
$%&'()*$+,*-
'8(0\1-!-EM)'„ &^T')$>! \^T
T<;$>Y \^TK-(i#HDu1-0(P
"f&&1='8<)!>rc,
_;$>-?-1$>::T\! K&H
>P-x%"#$B)T"8U%#l
$>.'8)!>&:T%#l$>.%y$=)!>
&(0-x) TX<)!>HD.>A)%"#$
%E('0$--0,(b$"U05e5eHV
T1(-E%E(#)X _H
Sr9!:3;<(%E('0-\
%;$<-E($0,T%$) -,PA)J%E(#j
-=-E%E(#T"1k-E($K,(6I-
:$
M4gDZ!
-S[4567
90538z}+~>
-S[Nx3
5_90}+~?
DE($ aVA aVc
E(#j-= [•=€c+
"S3[•=€c+•=€=a) -,T"1-E($K0%P,l
i\0-'c '8-'8H
%%E('0$-0,('8-'8W
5rz
3qz4EF
4E1S74\7
NB90
\7NB90
3qz4EF
wFD4\7
NB90
g05e
ZLQ[
h
S!>&,'0)bA)B
-C#-x&H
h
g05e
ZLQ[
h h
./012&3415 !"#$%&'
!"#
$%&'()*$+,*-
OBP*+ ?'AQ+@/
G%E('0-%E(%< Y'c-f$^(H
G%E($-%E($'8@\M(=.]&
:?KE$##^#==>?@K05e5eH
D;'I?'$'/
Q$%)!>I &"\P%E(Y(H
‚0:IN'1RASA+ƒ
AV,<„-v"-#
PBTN'1I;>%
UV%Q+@/
\$?\?$-1$RK,(T1(\,(
-#H
.-#J!WXYZ .-#J0WXOZ
V *H6 5H6
?# *H6 4H6
.-#& +H2 2H*
:+@[ H H5
PBY\)3Q+@/
7J%E(#j ?$%E(k,(N
0DO$-H
N "1?$,…'-x,T %;$<%E(
H$>"\]'E-'%$=%'T1J%E(#
j-=H
Tw\95N3qz4ED90p…95p|3`3qz4EFwFD4\7NB90
x375_90‚+~?ƒ 56790538z‚+~>ƒ
./012&3415 !"#$%&'
!"#
$%&'()*$+,*-
+H2 2H*
Bb87575D†9 H H5
3\4E‡7QFW4ˆw4 ]B]]]Y]
Bb87503\4E‡75D†9‚ƒ ]B]
G<%"U"#(B%;$<0'0-'8
-'8HQ$-J%E(#j-= %;$<~6\6666†6\6+
Y>T"1k-E($K05eZT1([05eZ0-
#[$JG^#"1%;$<-E($K05e 8
-E($05e%Pb$"() %;$<K-H
O"1?$$R
−
= =
(7,6 5,7)
SMD 0,90
2,1
<"$:O j\•=€+= Y>(#-<'UK)!>&,
A) 5l90Nm9045_7En40o9p3qD45_77r75_F7s945_7pt75F3-%i^\
'8< #^#=K&0T1(5e+6B
A9B-&+C
pF1A) 5l90Nm9045_7En40o9p3qD45_77r75_F7s945_7pt75F3
'8 05] &05'VLOQ?Y<
G{$>1-'c%i^\'8< #^#=q-x-'c
%E(#HH
./012&3415 !"#$%&'
!"#
$%&'()*$+,*-
GE$-M -E($K05e\5e'0$-H
H|9bDt9
;$<K%E($-K,(T1(&_`Ba%;$<
%E('8#K,(-#&_bB`HD"1-E(k
,(TBBD.$-, Y>-E(GK0-#T1(-x,T
%1|1\0-'c-,-E(G 80-#H
O"1?$$RK%E("Vc_]B]BD.$>,
i(#-<'UK-+6B
7J%E(#jDG$-K0\_]B]]]Yd]e]bB;$<
>%C-?T"1DGK,(%P<b$"()
-H
D;/
N"#$>A)5l90Nm9045_7En40o9p3qD45_77r75_F7s945_7
pt75F3-%i^\'8< #^#=K&0T
1(5e+6B
$>"f0&'(B-C#-x-'c&U0
4"1=)B-C#-, E$##^#=_
!H
0"D*EC
./012&3415 !"#$%&'
!"#
$%&'()*$+,*-
Of]&KB-C#-x-'c&U04
? &B-C#-x-'c=) E$##
^=HL'0)b&=) !B-C#-E-z
]&E$#H
aVI-#":I!
bBT4;+/
;$<)!>(P 5U'VLOQ\P-x]-'c(%
1(` 1WA)5l90Nm9045_7En40o9p3qD45_77r75_F7s945_7
pt75F3 '8 05m]j(,%i^\'8<
;$>8 ]&E$##^#=H
aV?41;#/
}1FG5A"W,E‡c"(%: "%(-M)r)!>&H
}1FG!GW%PT&\TM)'„.:-E<)!>H
GT&1=cl&=)%#-x&-E(V<
m$>-'c-::T\! K&H
F0%;$<K -x-'cP;$< $=\,lKz 'V
LOQ?YP( B!-M1;$9(\…-u1
"<)!>(P 5,E#) > 1)!>&-E! #
]9 %#(P &\,f9 Y'c %
$Y$>E 06^(&636+H
./012&3415 !"#$%&'
+
!"#
$%&'()*$+,*-
$>" ;$$=)k1$\T1 %PE
%`$,H•Y( T-,,9(%< L-M% &H
9&(8H
<G>626^(6
N'VT1
N$>XG:>
-v
H Q % (P 5NnG/ )H
H Q%<3NnGLNH
H 1$=$YN"#$% &'!(#)3G/SoDH
STF13Ga66H
H 1$=$YN"#$% &'!(#)6636H7_
/SoD<GH
+H ˆjW$jj$%(H (H
*H ˆjW$j)j$H%(H (H
2H ^<a-! $>"(PK/SD<GH
4H 79'8LOQP 7_/SD<GH
./012&3415 !"#$%&'
*
!"#
$%&'()*$+,*-
-@!
Ih/G"#
/$%-u+~>
G2H
$f)!>W*
N>)!>W+H65H
@V!
@V@3M945_7!
LQ%A(b$KE$#Y>^^#U(b$H
LQE$cA)J-z"H
@V?‰9s90W
LQT1-'c%i^%A(b$KE$#Y>^^#U(b$
LQT1! %A(b$^#U(b$H
@V>5\3NB!
,;$jW: R=\:I
:W/S:T &=H
?VG#!A(b$KE$#Y>^^#U(b$H
>VŠ!
"WG<Cz;$1=H
WG<\$R?j >"$f$K'0H
AV‹/G#!
AV@‹9N‡954Œ75_7L|`3qzC389 WE()1%E(T$R?UK
LQ
AV?3qz4EFz3890!‚A[5ƒ
"T/FP#z;$-E%A(b$KE$#Y>^H‰)%A(b$E$
#
Y>^W
5
Š
+6 *
H
93IWFP#'Q/e4
‹)W
H * 5 5 H
Š
+6 +6H 6 * * *
= = = =
H
H
H H H
"Y/FP#z;$^#U(b$H‰)^#U(b$W
+
−
93IWFP#'Q/e5
‹)W
( ) ( )
( )
( )
( )
+ + +
= = = +
−
−
./012&3415 !"#$%&'
2
-:v#
!"#
$%&'()*$+,*-
4.3 3M94E…95p|35o7 !
G•" G
* : T/Z[ F W /F 0
1$(0
*:Y/~jFp|34t[!Z+[
k743XD! LQ=)-'cJ
-z-8<^=H
.!/&LQ"A=4\5e
5Q/
JH3:BW
4 e Š 5 e }
+6
LQ"A=+6\+)e6Q/
EW
1 2
50 / ; 52 /
3 20
ab
c d
a b−
./O &=IJ,l\$-,
=IJ-
"/QA =$(
./$%A(b$E$#Y>^
(' d
*:O/~-DP894t[‚?=[5ƒ
k743XD! LQ=)!
J-z-8<^=H
./D' =+\)\+e6Q/
"<H
"/•$=
.F0>A)%#
-E]&
"/•$>-M\J%'8\B
-C#
=
K K
\-'
)Y$^\9:9A
./O LQ"<>\LQ
%( =
"/N=IJ("<\/F
=IJ-
~jFp|34t[
H+ *+ *+
4 e
+6 +6H+ 56
56
5 e
= = =
+
+ = = +
H
H
H
H H H H
= = =
1 1 5 5
50 /
30
3 20 6 5 6 5. 5
c
( )
+
=
−
−
2
2
52 /
ab a b
ab
d
a b
a b
.6/$%A(b$E$#Y>
^-z(b$KE$#.
)!'8K uE$
#M)J%'8-E
-' )Y$^H
~-DP894t[
S!Wn40o9p3qD45_7
5+)*LMHN/OM?#A
( )
2 2
2 2
2 2 2 2
2 2
2 2
1 1
) 1 1
1 0
1 0
)
a b ab
b ab ab a b
a b a b ab
a b neáu ab
a b neáu ab
a a b
a ab
d a
a b a b
+
+ = = +
+ >
=
− + <
+
+
= =
+ +
5+)*LPHOM?#A
./012&3415 !"#$%&'
4
!"#
$%&'()*$+,*-
./ D' =++e6Q/"
<
"/•$=
./ ‰ ) ;$> -'
)Y$^M,(!A-E-u
9A$
"/g( =Y(-E(
./ O &"<A\(‡
j((9$
"/ N= IJ ( "<\/F
=IJ-
./ D' ="<H#D*
Q*R!4/<
+ Š Š * Š 26
"/=$]l;$
./,E)r'8 -E
Q
"/D' )Y$^M
./O LQ"<>\&
%( =Y(-E(
=\&"(=H
"/N=IJ("<\/F
N=IJ-H
./D' ="<W
+ * 5− =Q Q
%IB
‰HŠGHŠOH5ŠSH4
"SB(.93IT
"/O]l;$ j'0
)bH
./O LQ< $=,(% <
]
"/D!)1,(",<
:H
"/N=IJ,l("<H
.N=IJ-H
( )
+
+ +
+
−
−
= = −
− −
S!W5Y94d7545|9595Y94j
5+)*LLOM?#A
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
( )
[
[
+ + +
= + + +
= + + +
= + +
− + −
= − + −
= + − +
= + − +
= + −
H H
H H
H
H
H Q B Q B QB
Q Q B B Q B B Q
Q Q Q B B B B Q
Q Q B B B Q
Q B Q B
S!WR[ŽM[45ˆT45_464s90CO9
+ 2+ Š Š * += = =
,W
+ 26 2+
5 26 +
< < <
< < <B
S!W…zŽp3M4
5+)*LUOM?#A
O&SH4
+ * 5 + 5
5
4
− = ⇔ − =
⇔ =
⇔ =
Q Q Q Q
Q
Q
5. T Œ90`M4L|51S90C•95o74t[!‚a[5ƒ
aV@VŒ90`M4!
./012&3415 !"#$%&'
5
!"#
$%&'()*$+,*-
-:/!*"A-(9-6ER+6AfB
>@
5V*WXC =YH@
Z
[
Z
YZHYH
Z
Z@
5V*W\C =0H@
Z
[
Z
0ZHYH
Z
M@
"\HV*WC
Z
]H
Z
[=YH@$=]H@
P@
^)**WXC =YH@
M
[
M
YM
Z
HYMH
Z
YH
M
L@
^)**W\C =0H@
M
[
M
0M
Z
HYMH
Z
0H
M
_@
X3)**WC
M
YH
M
[=YH@$=
Z
0HYH
Z
@
U@
"\3)**WC
M
0H
M
[=0H@$=
Z
YHYH
Z
@
&;?JQ(9-6R+6AWg*
FZ?;6J$/
( )
( )
( )
( ) ( ) ( )
( )
( ) ( )
( )
( ) ( )
[
[
[ H
[ Z [H
+[ Z [H
*[ Z [
2[ Z [
H H H
H H H H
H H H H H H
H H H H
+ + = +
− + = −
− = − = + −
+ = + = + − +
− = − = − + +
+ = +
+ = +
aV?1S90C•95o74t[!
ŒD0&U&>W
L&=%iP#-' )Y$^\-' )Y$^\%A
(b$E$#Y>^\^#
nj(!=-x(!0&$0
g(=+\\+\\)\j\+*e6Q/
ŒD0&U&j W
‚=LD-x&HO$R?p`T(HH)q,
=)LD-0H
cH5kbk7!
Ih/G"#
/$%-u+~>
./012&3415 !"#$%&'
6
!"#
$%&'()*$+,*-
G4H
$f)!>2
N>)!>W6H6H
@V!
@V@3M945_7!
LQc%i^-zE$##^#=H
LQE$]&E$##^=H
@V?‰9s90W
LQT1-'c%i^-zE$##^#=-E<
";$H
LQT1! %i^]&E$##^=H
@V>5\3NB!
,;$jW: R=\:I\>"$:(PH
:W/S:T&H
?HG#!•]&E$##^=H
>VŠ!
>V@"WG<\G
>V?W‚=J-z^#=\<,(H
AV‹/G#!
AV@‹9N‡954Œ75_7L|3qzC389WE()1%E(T$R?UK
LQ
AV?3qz4EFz3890!‚c[5ƒ
D. ‡Zs[-E P#$W
"T/93IC
./012&3415 !"#$%&'
•4H'&(#
!"#
$%&'()*$+,*-
e HHH
e H HHH
e HHH
e HHH
+e HHH
HHH
=
=
=
=
=
= −
K
K 5
K
5
K 5
K 5
K 5
"Y/
* e HHH
2 e HHH
4e HHH
5e HHH
=
=
=
±
=
±
K
5
K
5
K 5
K 5
./O LQ)'00=IJ(\/F=IJ -E(H
AV>3M94E…95p|35o7!
G•"" G
*:TB=>*@%+!H+CA%\H+
TU4NB90?!"dCk@W•]&WZ[
k743XD!LQ]&E$##^=
./ Ž"$f$LQIQ/\/F:)"
<
"/•$:)
./F0•6^# $,iH
./G-f$T1J d
"/D' )Y$^%A(b$
KE$#Y>^
./O LQ-#!‡<V\/F<H
3TW•]&W
4
5 6 5
4
a
a a
a
+ − +
0≥6
= + − +
= + − + = +
6 2
5 . 5
2
5 3 2 5 6 5
a a a a
a
a a a a
./012&3415 !"#$%&'
0‰HHHGHHH
0‰HHHGHH
0GHHH
0‰HHHGHHH
0‰HHHGHHH
( )
( )
* e Z 6Š 6[
2 e Z 6[
4e Z 6Š [
5 e Z 6Š 6Š [
= ≥ ≠
= >
= ≥ ≠
−
±
= ≥ ≥ ≠
−
±
m
m
K
K5 K5 5
5 5
K K 5
5
5
5
K 5
K K 5
K 5
K 5
K 5
K 5 K 5
K 5
K 5
e
e H Z 6Š 6[
e Z 6Š 6[
e Z 6[
+e Z 6Š 6[
Z 6Š 6[
=
= ≥ ≥
= ≥ >
= ≥
= ≥ ≥
= − < ≥
K K
K 5 K 5 K 5
K K
K 5
5
5
K 5 K 5 5
K 5 K 5 K 5
K 5 K 5 K 5
!"#
$%&'()*$+,*-
./O LQ(•@
"/LQ"<T1\)'00(
= =IJ
./O LQ(:)\/F:)"<
./DE#(-C#( d
"/&;H*I;>%Y?;(
./8-'*;HB
"/h
Y
U&
Y
?'Whi&Z
Y
./O LQ(•?\ <
TU4NB90?!-DP894t[‚@a[5ƒ
k743XD!LQ#(-C#H
.,G/ &;H8?j(
9h
O
i&
O
B
"/LQ( =H
./O LQ"<>\LQ%=
IJH
./ O LQ (:)Z -'"<
[
O E$#W
2
1 1 1
.
2
2 1 1
a a a
P
a a a
− +
= − −
÷ ÷
÷ ÷
+ −
F0•6≠
[•]&E$#7
[(?K-E7†6
./Lx>"$#TT1J: 7H
"/•$>-M u\$&\:t>
\:9
./OfA)LD -ET1d
•@•]&
− + +3 5 20 4 45a a a a
0≥6
( )
= − + +
= + = +
3 5 2 5 12 5
13 5 13 5 1
a a a a
a a a
3YWO#(-C#
( ) ( )
+ + + − =1 2 3 1 2 3 2 2
( ) ( )
( ) ( )
( ) ( )
= + + + −
= + + + −
= + −
= + + − = =
2 2
1 2 3 1 2 3
1 2 3 1 2 3
1 2 3
1 2 2 2 3 2 2
VT
VP
•?O#(-C#
( ) ( )
( ) ( )
( )
+
= −
+
+
= −
+
+ − +
= −
+
= − + = − =
3 3
2
2
a a b b
VT ab
a b
a b
ab
a b
a b a ab b
ab
a b
a ab b a b VP
( )
2
0 ; 0
a a b b
ab a b a b
a b
+
− = − > >
+
3OWQ/e
( ) ( )
( ) ( )
− − +
−
=
÷
÷
+ −
2 2
2
1 1
. 1
) .
2
1 . 1
a a
a a
a P
a
a a
− − + − − −
=
÷
−
2
1 2 1 2 1
.
1
2
a a a a a
a
a
( ) ( )
− − −
− −
= = =
−
2
1 1
4 1
.
4 1
a a
a a
a a
a a
[S •6≠"7†6%
./012&3415 !"#$%&'
!"#
$%&'()*$+,*-
./O LQ(•>ej ,(
ZD.-'"<[
.WQ$-,/F -!)1,("<
>H
"/S'00 =IJ
./N=IJ-
- F=)LD d
- LQ<V
a%
−1 a
a
†6⇔3†6⇔•
•>e•]&E$#W
( ) ( ) ( )
− + −
−
= =
+ + +
= −
2
2
2
3 3 3
3
)
3 3 3
3
x x x
x
a
x x x
x
−
−
1
)
1
a a
b
a
0≥6\≠
( ) ( ) ( )
− − + +
= =
− −
= + +
3
3
1 1 1
1 1
1
a a a a
a a
a a
aVŒ90`M4L|51S90C•95o74t[‚@a[5ƒ
aV@Œ90`M4!
/FWO LQ(=+4e\+5eQ/
•]&W
1 1
5. 20 5
5 2
+ +
3 2
5 4 25 5 16 2 9a b a a ab a− + −
LQW(Y(-E(=\&=HLQ
"<>H
/FWO &=IJ(\$-,
F"=IJ-
/FWO LQ(=*6eQ/Z-'
"<[
O E$#
16 16 9 9 4 4 1B x x x x
= + − + + + + +
[•]&E$#G
[(I G,?*H
/FWO LQ !-,(% <]$
-,-!)1,("<>H
G=+4eQ/
+ + = + +
=
1 1
5. 5 .2 5 5 5 5 5
5 2
3 5
G=+5eQ/
− + − = −5 20 20 6a ab a ab a a a
G=*6eQ/
= + − + + + + +
= + − + + + + +
= +
+ = ⇔ + = ⇔ + =
⇔ =
) 16( 1) 9( 1) 4( 1) 1
4 1 3 1 2 1 1
4 1
) 4 1 16 1 4 1 16
15
a B x x x x
x x x x
x
b x x x
x
F=>I~+
aV?V1S90C•95o74t[!
ŒD0&U&>
F.Ij(!:)\•-x(H
g(=+4Z\)[\+5\*\*e\Q/
ŒD0&U&j W$&$>1=,=)LD
cV5kbk7!
./012&3415 !"#$%&'
!"#
$%&'()*$+,*-
Ih/G"#
/$%-u+~>
G4H
$f)!>W2
N>)!>W6H6H
@V!
@V@3M945_7!
LQc%i^-zE$##^#=H
LQE$]&E$##^=
@V?‰9s90W
LQT1-'c%i^-zE$##^#=-E<
";$H
LQT1! %i^]&E$##^=H
@V>5\3NB!
,;$jW: R=\:I\>"$:(P
:W/S:T&
?HG#!•]&E$##^=
>VŠ!
>V@"WG<\G
>V?W‚=J-z^#=\<,(H
AV‹/G#!
AV@‹9N‡954Œ75_7L|3qzC389WE()1%E(T$R?UK
LQ
AV?3qz4EFz3890!‚c[5ƒ
$\^#-M)!( d
‹)W•]&
6 + 4 2 Š 6\ 66 6\64 6\ +6
− + + + +
%+ W$\^#-M)!\1k$>"
^#H
./012&3415 !"#$%&'
+
-:v#
