4رياضيات رابع علمي2011-2012
DESCRIPTION
MATH for Grade 10TRANSCRIPT
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5 : cigol lacitamehtaM
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11 tnemetats lacigoL
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) 1 - 1 (
P P )eurT( )T(
P )eslaF( )F( P
P
) 1 - 1 ( .
P P
T F
F T
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6 )( )(:
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21 ( neht fI
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) tnemetatS dnuopmoC (.
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. )) .... (( .
) ( )(
. :
) .... ( .
) (
) ( .
Q P Q P
T T T
F F T
F T F
F F F
Q P Q P
T T T
T F T
T T F
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1(
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3(
4(
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) .... (
P Q : Q P .
)) P Q ((
Q P :
)4-1(
Q P .
PQQ P
TTT
TFF
FTT
FFT
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8 1 :
1( 3 X , 2>X
( 0X , 02X
( P : Q :
( 2=X 8=3X
( 2>X 5>X
(0 2X 0X
( P Q
, 2 = X
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11
stnemetatS tnelaviuqE
)1-1(
P Q Q P
4
QP ~QP
:
Q P~ Q P P ~ Q PT T F T T
F F F F T
T T T T F
T T T F F
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21
) 1 - 1 (
1
:
( 5 52 7 52 .
( 5 52 7 52 .
( 7 4 .
( .
( .
2
:
Q P
0=b 0=a Rb,a , 0=b.a9 = 2X3- = X
5 = X52 = 2X
2 = X8 = 3X
0=)2-X()1-X(2=X 1=X
-
31
3
:
1 ( P~ Q~ QP
2 (
3 (
4 (
4
P Q S
1 (
2 (
3 (
4 (
5
: -
P Q S :
1 (P~ P
( P P ( P P ~ ( P~ ( P P~
2 ( S S
( ( ( (
3 ( 3 + 5 > 9 S~ : -
( 3 + 5 9 S~ ( 3 + 5 < 9 S~
( 3 + 5 9 S~ ( 3 + 5 9 S
Q~P )QP(~
)SQ~(P~ )SQ~(p
S )QP(
P )SP(
P )QS(
S )SS(
)SP~(Q~ )SQ~(p
-
41
51[ secnetneS nepO
) ( .
:
( X
(
( b a
( . . . . .
.
)( 9 X )9 (
)Y( )( . b a 3
)3+3=6( . )(
.
)2-1(
1(
.
2(
.
61[
:
)Z(
}2{ }2{.
.
)X(P
)Y(Q3=1+Y
)b,a(G6=b+a
4=X2 :)X(P 1=1-X :)x(Q
)X(P )X(Q
)X(P,)X(Q
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51
5
Z .
}2{
} { }2{ } {
.
)3-1(
.
6
Z .
4=2X:)X(Q
2=X:)X(P
)X(Q,)X(P
)X(P
)X(P2-,22-,2)X(Q
)X(Q
)X(P)X(P
)X(P)X(P ~
0=4-2X
X
61+X 4=X
04-2X
X
6=1+X 4X
)X(P)X(P ~
-
61
) 2 - 1 (
1
:
( 3 3 , 0=)2-X()1-X(
0=03+X11-2X }3 , 5 , 6 ,01{
4>X 0=)5-X()1-X( N
-
71
3
} 5 , 4 , 3 , 2 , 1 {
( 4=X2
( 7=4+X
(
( 92X 4=2+X
( 61=2X 4=1-X
4
Y X : } 9 , ........... , 2 , 1 , 0 {
( 3=Y-X
( 51=Y+X
0=)4-X()3-X(
-
81
71[ snoitisoporP dereifitnauQ
]1-7-1[ :
:
: A :
a A
A a
:
.
) (
.
:
X :
: A :
A
:
Ab ) (
Ab
2=1+X Z :
ZX 2=1+X
:
ZX 2=1+X .
)X(F
)a(F
)a(F
)a(FAa
)a(FAa
1+X2+2X=2)1+X(
NX 1+X2+2X=2)1+X(
)x(G
)x(G
)b(G
)b(G
-
91
]2-7-1[ : :
:
.
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:
.
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2 6 :
2 6.
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.
.
:
Xx )x(P ~ ] Xx )x(P [~
Xx )x(P ~ ] Xx )x(P [~
7
:
1( X :
: X 0 > X 2( X : : X
3(
)X(P
)X(P
)X(P
)X(P] 53+X : RX[ P
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02
1( ) ( ~ ) ( P ~ : 0 x : .
2( )X( ~ ) (P~ : X : X
X .
3( ) (
]3-7-1[ ygolotuaT : P P
.
8
P P ~P
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: ) noitcidartnoC ( .
P ~P P ~ P
T
F
F
T
T
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X P
XX
X P XX
P
XX
R X : 5 < 3+X P
X ] X )X( [ ~
] ) ( P [ ~
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12
)3-1(
1
:
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(
(
2
:
( X ) ( P :
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( X )X( :
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( X )X( :
)X( : X 2X .
( P Q : .
( P : PP ~
( Q P : ) Q P ( ) Q P ( .
P ) 8 < X : RX (
X
P
P
XP
P
P
Q P Q
52 = 2X : N X :Q
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222222
Gd Gdf : M GC YGO Gd 2 ]1-2[
]2-2[
]3-2[
]4-2[
]5-2[
]6-2[
]7-2[ |X|= Y
]8-2[
]9-2[
]01-2[
]11-2[ ) (
]21-2[
-
32
: srebmuN laeR fo dleiF
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12[ snoitarepO yraniB
)N(
: )b , a( N N b a b + a .
N N N
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A A A A
A
: P A .
A A A : P
AA )b , a( A )b , a( P
1
+Z a = b a Z b a . +Z
+
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42
:
2
: = b + a 4 .
A
:
Ab a Ab a A .
0123
00123
11230
22301
33012
+Z 01 =01 01 , 7 = 1 7 , +Z 3 = 5 3
+Z b a +Z a = b a
}3,2,1,0{ =A
Ab a b a
-
52
3
N : Nb a b - a = b a. N
( b a b a = N .( b< a b a = N .
N .
)2-2( : metsyS lacitamehtaM
.
A ) , A (
A ) , , A ( .
: , , , )+(
, )-()( N.
)+,Z()+,Q( )+,N()+,R(
),N()-,N(
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62
22[ puorG
.
)3-2(
) , A( : 1 ( ) , A( metsyS evitalumuccA
A c b a :
c ) b a 2 ( tnemelE ytitnedI
Aa A e a = e a = a e 3 ( ) , A( metsyS cirtemmyS
1
Z .
: )1(
.)2( A ) , A(
. A
) , A( .
e
e= a a = a a A a A a
(=)c b( a
)+,Z(
-
72
1 ( )+ , Z(
Z c b a
2 ( Z a a = a + 0 = 0 + a
)+ , Z( )0(
3 (Z a 0 = a + ) a -( = ) a -( + a
)+ , Z(
)+ , Z( Z
)+ , Z(
2
) , N( .
c b a = c] ba [ = c ) b a)b( ]a [ = ) cb ( a = ) c b ( a
c
)c b ( a c ) b a () , N(
)2( )3(
c + ) b+ a (
Z 0
Z a -
=)c+b(+a
N c,b,a(
-
82
112[
)1(
) , A( : e ) , A(
e
: e ..... )1(
e .... )2(
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2(
meroehT noitaiverbbA .
: A c b a
a a
c a = b aa c = a b
e =e e e =e e
A c,b,a
c=b
c=b
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92
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b )a a( = c )a a( b e = c e )(
b = c ) ( ). . (
2 (
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A a a
a r
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.... )2(
a r = a a r = a
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e=a ae=a r
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b = y a b a = )y a ( a
b a = y ) a ab a = y e
b a =y ). . ( )2(
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) , A( A b a 1 ( = ) a (
2 ( a = )b a( : )1( e = ) a( a
e = a a a a = ) a( a
). . (
)2( ) ( ) b a(
e = )b a ( )b a( ] )b a ( a [ b = )b a ( ) a b(])b ) a a ([ b =
A a A a
(
a
b
.... )1(
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A a
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b
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13
b b= )2( .... =
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a b = )b a ( ). . (
3
Z :b a - b + a = b a
) ( )( .)( 9
) ( 0 = e
Za a = a e = e a
a = a = a
)( b 9
0 = 9 b - 9 + b = b 9 - b + 9
0 = b 8 - 9
Z = b 9
98
e
Zb a
]b e[ b=
)b a( ) a b(=)b a( )b a(
a =a 0 -a +0 = 0 a- 0+ a
e =9 b =b 9
-
23
)1-2(
1 /
) , A( )+ , A(
2 /
:
)+ , N( :
( + N (
( + N ( 3
3 /
:
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( .
( ) + , +Z ( .
( ) ,A( : 2b + a = b a
12
}1-,0,1{=A
) ,}1-,1{(
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33
4/
) , Z( Z : Z b a 2 + b + a = b a
( )2-( .
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( 1 = X .
5/
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+Q
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43
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1
+ N .
N .
) ( )5 4( + ) 5 3 ( 5 ) 4 + 3 (
)( )4 5 ( + ) 3 5 (
) ( )5 4 ( + ) 5 3 ( 5 ) 4+3(
= )02( + )51( = 5 7
= 53 = 53
)5 4 ( + ) 5 3( = 5 ) 4 + 3 (
)( ) 4+3 ( 5 ) 4 5 ( + ) 3 5 (
= 7 5 = )02( + 51
= 53 = 53
) 4 5( + ) 3 5 ( = ) 4 + 3( 5
)4+3( 5
-
53
) 4 - 2 (
A A :
1 (
2( )c b( c b a A
:
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:
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63
2
1 ( 2 ( + N
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3
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73
42[ gniR
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4
: Q .
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2( + Q3( : c a + b a = ) c + b ( a
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: Qc b a
:
.
) , , A () , , A (
) , A (
) , + , Q (
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0QQ a ,a + 0 = 0 + a a =
, Qa - Q a
) , + , Q (
Q
) c + b ( + a = c + ) b + a (
= )c b( a c ) b a(
-
83
5
: .
: :
1( N 2( + N
3(
3 , 4 , 9
) 4 3 ( + ) 9 3 ( = ) 4 + 9 ( 3
)1( + )3( = 31 3
41
+
) ( )( .
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) c b ( a ) c a ( + ) b a( =
-
93
52[ dleiF
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)(
+ ) ( a a- .
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a 1- a .
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:
1(
2(
3( +.
)7-2( :
) 0 { /A { , () + , A(
b a A1 ( b + a A
2 (
a b = b a3 ( a + b = b + a
4 ( A a
a = a + 0 = 0 + a
A aa = a 1 = 1 a
5 (
0 = a + ) a - ( = ) a - ( + a
} 0 { /A 1-a Aa
1 = a ) 1-a ( = )1-a ( a
), , A(
) , + , A(
)+ , A(
) , }0{ / A(
A 1A 0
A a - A a
) c b ( a c ) b a (= ) c + b ( + a = c + ) b + a (
-
04
____=X1
____=X
)( )+(
6
Q
.
)( )+(
.
1(
2(
3(
4(
a = 0 + a = 0 + a
Q a
5(
0 = ) a -(+ a = a +) a
:
}}0{ / Q { a
}0{ /Q{ 1- a
1= 1- a a = a 1- a
}0{ / Q a
) , + , Q (
) ,+,Q(
) ,+,Q(
)+ , Q(
)+ , Q(
)+ , Q(
) , Q(
) , Q(
) , Q(Q 0
) , + , Q (
: )1( :
a 0 = 0 a
)2( :A b a
0 = b a 0 = a 0 = b
A
a=a1=1 a
Q a-
-(
Q a
Q 1
-
14
7
) , + , Q ( :
3=1+X3
)1(
2=0+X3
2=X3
= } {
)1-(+3=)1-(+1+X3
)1-(+3=))1-(+1(+X3
1 )2( ____ =)X3(____3
13
1)2( ____=X)3. ____ (3
13
____=X1
____=X
23
223
3
-
24
)2-2(
1 /
1( ) , +, Z ( Z .
2( ) , - , N( N .
3( ) , + , R( R .
2 /
1( ) , + , E( E .
2( ) , + , Z( Z .
3( ) , + , K( K .
3 / )( )( :
1( ) , , A( e
2( :
3( ) ,A( 4/
) , , R ( :
5/ :
1( 5=1+x2 ) , + , R (
2( 3=2+X5 ) , + , Q (
) , } e {/ A(
A c , b , a) , } e {/ A()cb()ca(= c)ba(
),, A(
1+b+a=ba a + b + ba =b a , Rb , a
-
34
62[ snoitaleR
.
.
:
noitaleR evixelfeR
) 8 - 2 ( :
r A :
1
A
r = } ) 2 , 2 ( , ) 3 , 3 ( , ) 4 , 4 ( , ) 5 , 5({ . 1
1(
r = } ) 2 , 2 ( , ) 3 , 3 (, ) 5 , 5({ . 2
2(
r = } ) 2 , 2 ( , ) 3 , 3 ( , ) 4 , 4 ( , ) 5 , 5 ( , ) 4 , 3 ( , ) 3 , 4({ . 3
3(
r = > . 4
4(
r = . 5
5(
Aa r ) a , a(
} 5 , 4 , 3 , 2{=A
-
44
r = . 1
1(
r ) 4 , 4 ( .2r =
22(
r = . 3
3(
r = > 4
4(
r = . 5
5(
noitaleR cirtemmyS
) 9 - 2 ( :
r A :
2
A
r = }) 3 , 3 ( , ) 4 , 4 ( , ) 5 , 5({ . 1
1(
r = }) 4 , 3 (, ) 3 , 4({ . 2
2(
r = } ) 4 , 3 ( , ) 3 , 3 ( , ) 4 , 4 ( , ) 5 , 6 ( { . 3
3(
r = > . 4
4(
r = . 5
5(
r ) 2 , 2 (4
r)b , a( r )a , b( A b , a .
} 6 , 5 , 4 , 3 {=A
-
54
r = . 1
1(
r = . 2
2(
r ) 3 , 4 ( .3r =
33(
r ) 3 , 2 ( 4r =
44(
r = 5
5(
noitaleR evitisnarT
) 01 - 2 ( : r A :
3
r = }) 6 , 3- ( , ) 6 , 4 ( , ) 6 , 1 ( , ) 4 , 1({ . 1
1(
r = }) 4 , 1 ( ,) 1 , 3- (, ) 6 , 3-({ . 2
2(
r = } ) 4 , 1 ( { . 3
3(
r : . 1
r : : 2
r: ,r : ) b , a ( :3
) c , b ( ) c, a ( .
) c , b ( .
r ) 2 , 3 ( 4
r ) 3 , 6 ( 4
r ) 6 , 3 ( 5
r)c , a( r)c , b( ,r)b , a( A c , b , a .
} 6 , 4 , 1 , 3- {=A
r )4 , 3-( 2r )1 ,3-(
2r)4 , 1( ,
2
-
64
noitaleR ecnelaviuqE
) 11 - 2 (
r A
.
4
= }) 1 , 1 (, ) 2 , 2 ( , ) 3 , 3 ( , ) 2 , 1 (, ) 1 , 2 ({
= }) 1 , 1 ( , ) 2 , 1 ( , ) 2 , 2 ( , ) 1 , 2 ({
= }) 1 , 3 (, ) 2 , 2 ( , ) 3 , 3 ( , ) 2 , 3 ( , ) 1 , 1 ( , ) 3 , 1 ({
: .
: .
: .
r 1
r 2
r 3
r 1
r 2
r 3
} 3 , 2 , 1 {=A
r )3 , 3(2
r )2 , 3(3
r )3 , 2(3
-
74
noitaleR cirtemmysitnA
) 21 - 2 (
r A :
5
:
1( : B A .
: N . 2(
3( = } )1 , 2 ( , ) 2 , 1 ( , ) 3 , 4 ( { .
1( B A A B
.
2(
.
3(
1 2 .
,r) b , a (
b = a r) a , b (,
r 1
r 2
r} 4 , 3 , 2 , 1 {=A 3
B=A
r 1
ba ab b = ar
2
r )2, 1( 1 23r)1 , 2(
3
r 3
-
84
noitaleR deredrO laitraP
) 31 - 2 (
A :
.
6
r N .
1( r .
2(
r .
3(
r .
r .
} b a , N b , N a : ) b , a ({ = r
a b , b a b = a
c b , b a c a
-
94
7
r / .
.
1( r :
2( :
3( :
r .
noitaleR deredrO latoT
) 41 - 2 (
A
:
Ab,a
a/a ,+N a
b/a a/bb = a ,+N b, a
b/a c/bc/a ,+N c,b,a
r)b,a(r)a,b(
-
05
8
.
) 6 ( .
: 1 2 1 3 1 4 1 21
23 24 221
34 321
421
A .
9
/
(
(
(
: 9 2 9 6 6 2
} 21 , 4 , 3 , 2 , 1 {=A
} 9 , 6 , 2 {=A
a/a , Aab/a ,a/b b = a , Ab,a
c/b ,b/a c/ a , Ac,b,a
-
15
)3-2(
1 /
:
= }) 1 , 1 ( , ) 2 , 2 ( {
= }) 3 , 3 ({
= }) 1 , 2 ( , ) 2 , 3 ( , ) 4 , 3 ( , ) 1 , 3 ( , ) 2 , 4 ( , ) 1 , 1 ( , ) 2 , 2 ( , ) 3 , 3 ( ,
) 4 , 4 ({
) (
.
2 /
r N
}
3 /
A :
1( .
2( .
3( .
4( .
5( .
} 4 , 3 , 2 , 1 {=A
r 1
r 2
r 3
ba,Nb,a:)b,a({ = r
}3 , 2 , 1 {=A
-
25
2 7 [ eulaV etulosbA
) 51 - 2 (
X |X| :
0 >X ,X 0 = X , = | |
0 < X , X-
1
:
( ( | 3-X | R X
( 3 > ,3-X ( 3 = X, = | |
,3 +X- ) 51 - 2 ( :
1(
2(
3(
4(
5(
= | | 0 Y
6(
7(
]
]
XY
|X||Y|
:
Y X
.
RX 0| X | RX| X | =| X- |
RX | X | X| X |-
RY,X | Y | . | X |=| Y . X | RX , 2X =2|X|
RY,X | Y | + | X || Y + X | RX, 0a a | X | aXa-
x
>
0
3-X
X
0
3 3 01 = 01 3
01 < 9 =30 > 3 01 = 01 3
-
35
2
| X |=Y
| X |=Y
: X = Y .
: :
]) Y , X ( Y X
) 0 ,0 ( 0 0
) 1 , 1 ( 1 1
) 2 , 2 ( 2 2
) Y , X ( X Y
) 0 0 ( 0 0
) 1+ , 1- ( 1 1-
) 2 , 2- ( 2 2-
| X |=Y
) 1 , 1 (
) 2 , 2 (
X-=YX = Y
Y
) 2 , 2- (
) 1 ,1 -(
) 0 , 0 (X
0>X , X
0=X , 0 =Y
0
-
45
3
:
:
) X , Y ( Y X
) 3 , 1 ( 3 1
) 5 , 3 ( 5 3
) X , Y ( Y X
) 3 , 1 ( 3 1
) 4 , 0 ( 4 0
Y
X
) 5,3 (
) 3,1 (
)4,0 (
3+| 1 - X |=Y
3+| 1 - X |=Y
]]
1X, 3+)1-X(
1
-
55
8 2 [
4
: R X .
:
|6+X3| =
:
9=6+X3 } 2- X :X { .......
9 = 6 -X } 2- 0 X>2-
)2(
)1(
3-
-
65
5
: .
:
2 = X 8 = 3X 0 X , 0 = 8 - 3XS
1 }2 { =
2- = X 8 - = 3X0< X , 0 = 8 - 3X -S
2 }2- { =
S = S .1S
2 }2- , 2 { =
6
: .
0 = 21 - |X| + 2X :
0 = ) 3 - X () 4 + X (0 X, 0 = 21 - X + 2X 4- = X 3 = X
S 1}3 { =
0 = ) 3 + X () 4 - X (0< X, 0 = 21 - X - 2X 4 = X 3- = X
S 2}3- { =
S = S 1S
2}3- , 3 { =
0 = 8 - |X| 2X R X
0 = 8 - |X| 2X
0 = 21 - |X| + 2X R X
-
75
9 2 [
.
.
S 2S
1
S = S .1S
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S = S.1S
2
7
X Y :
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: )1( )2( : 6 = X 2 3 = X )1(
2 = Y
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= }) 2 , 3 ({.
R
-
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) Y , X ( Y X
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) 0 , 1 ( 0 1
XYY ,X
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50)0,5(
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0= 51+Y5-
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8
. Y X R .
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y
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: 0 = 6 - Y + X3
) 3 1 ( }) ) 3 , 1 ( })3 , 1({.
) Y ,X ( Y X
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94
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:
2
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-
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32
32
32
32
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3
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}
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:
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6
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R
R
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86
7
: 5
5 |5+X2| :
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5 -2
> 7> 7
> 701 X2 - > 21X
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>
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1 /
A - B B - A BA B A2 /
( 5 - | 2 + X |= Y (
3 / :
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( 51 = Y7 + X3 51 = Y + X3
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5 / :
( (
( ( 8 2X2 ( 0> 72- 2X3
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1= |3 + X4|
0 =4+ |X| X
92 = |4+ 2X|
4 |1+X| 21 |6-X| 3- 2 -| 3- X2| < 9-
1+x 3 = y
3 = 2+x xx = 1+x2
-
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Gd Gdd : GC S hGdhQ 3 ]1-3[
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3 (
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5 (
6 (
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.
.
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secidnI
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5 (
6 ( = n ) (
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stooR
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a ) nX RX (
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a =
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8- 2 4 3
59
n+m) 2 5 ( 2-m) 3 5 ( 3 5
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59
12 3
:
... m
.
a... m .m-
a = m)a -(m
1-= 52 )1-(
1 = 46 )1-(
n+m52 2-m51 521
m +n2 5 m57
m-2-m 3 m-n2-m2-n2+m2+2-m+3 5
= = 5 = 2-3 5 =
2= 2 1 = 2 1 3 0 = 8+2+9-2 3 4-4
n+m52 2-m51
m +n2 5 m57521
-
57
)1-3(
1 /
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( 0)8(+0)9( ( 1-)2(+ )3( ( 1 -)61( + 61 ( 46 3
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3 /
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:
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34
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x
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5 /
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6 / : ( 1 = x)z-y( a . y)x-z( a . z)y-x( a
(
7 /
: 1= +
8 /
: =
9 / :
01 /
: 72= ] [
1 c - b a + 1
1 b - c a + 1
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1 + n 3 + n+ 2 3
1 - n 3- n 3
n 2 72 1 - n 4 6
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n- 3 3
14
m
1n
nx1nx 1 2
11nx = n
-
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2 3 [
noitauqE laitnenopxE .
:
1( : )) 1((
:
2( ny = nx y = x n
y + = x n
3( n = m =
:
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1 = x 3 = 2 + x
= }1{
:
(
:
-
1 a , y = x y a = x a
my = nx
172 5
35
35
3- 3 = -)2 + x ( = -)2 + x (5
1 32x90 =
........0 = 91 2) (3x1 3x
3
1 + 3x3
0 =
1 = 3x : 31 = x
72
1 = 3x : 31 = x
72
3x . 3x = 32x
2) (3x =
1 32x90 =
........0 = 91 2) (3x1 3x
3
1 + 3x3
0 =
1 = 3x : 31 = x
72
1 = 3x : 31 = x
72
3x . 3x = 32x
2) (3x =
-
87
3
: 3+x4 = 1+x2- x2
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0 = 5 - x4- 2x
= } 5 , 1-{
.
4
: 18- = 2+x34 - 1+x23
3 0 = 18+ 23 x3 4 - 3 x23
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2 = x 2 3 = x3 9 = x3 1 = x 3 = x3
= } 2 , 1 { .
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1- = x 5 = x 0 = )1+x ( )5-x (
0 = 72 +x3 21 - x23
2
2
-
97
5
x : -
( 1-x5 = 1-x3 ( (
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1 = x 0 = 1 - x
( 2
1 = x 4 = 3 +x
( 2
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1-= x
6
R
-
6 2 = 6) 1 - x ( 45 = 5)3+x(
8x8+ 2
x+2
18 + 3
x8 + 2
x+2
241= 3
8x8+ 2
x8 2
18 + 3
x8 2
241= 3
8x8 +1 2
18 + 3
23
41=
8x41= ) (4 +2 +1 2
8x8 41= 7 2
x) (32 2 = 2
x38 2 = 2
xx3 12 = 2
22 = x 1 =
3
-
08
) 2 - 3 (
1 /
: ( = 3x ( (
( ( (
( 1 = 6+x5-xx ( (
2 /
R
3 / :
18 =
4 /
R x :
( 93 = 1+ x3+x3+1-x3
(
12
3x
172
12
12
2-x)72(1-x)342(
x )927(12
3 = )2+x( 2) -x( = 2) 342 5 ( 5
0 = 5+x52+x56- 63 = 2-x3- x6 001 = )5-x()4-x(01
62=)x-5+x5( 5 )1-x2(56 = 75-3+x22
0 = 3 9 - x 9 1+x 3
2
2
2 2 2
3+) (x2 4 + x4x2+ x4
52 =
-
18
12
3
53
n n n
55
12
3
x3
y2 = 3
x 3 3y 2 3
741 6 21 3 5
4 4 4
x
y
x
y
n
n
n
3 3 [
:
2 01 16
.
1. y x = y x .
: 27 = 21 6
3x51 4 = 3x 3 5
= o y.
: 7 = =
7
:
21 3 5 741 6
441 6 = 2 21 6 = 21 3
521 6 = 35 6 = 5
741 6 = 741 6
:
5
-
28
4 3 [ srebmuN etagujnoC
.
3 2 3
3 3
91 = 6 - 52 = ) ( ) (
2- = 5 4 - 2 9 = ) 5 2 + 2 3 ( ) 5 2 - 2 3 (
5 3- 1
4 = 1 - 5 = 1 - 521 3 = )1 + 5 3 + 52 3 ( )1 - 5 3 (
) (
8
:
+ +
+ +
+ + =
3 = 3 - 2 + 2 - 3 + 1 + 2 =
-
1
1 - 2
1
3 + 2
1
2 + 3
b + a
6 = 3 2 = 3 3 2
3 = 33 3 = 23 3 3 3
6 - 56 + 5
6 + 5
5 2 - 2 3 5 2 + 2 3
6 - 5
1+ 5 3 + 25 3
1
1 - 2
1 + 2
1 + 2
1
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1
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38
9
(
- 1-
1-
=
= =
(
2b -2 a
] b + a
]
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b - a
b2
]]
b - ab + a
b + ab - a
b + a b - ab + a
b + a - b + a b - a b + a
b + a b - ab + a
b - a b + a b 2
1+ 32 = x ,1+ 2 34 = y3 = yx= yx
) (1+ 2 34 ) (1+ 323) (1 + 3) (32 = 1+2 = 3 =
1+ 32 = x ,1+ 2 34 = y3 = yx= yx
) (1+ 2 34 ) (1+ 323) (1 + 3) (32 = 1+2 = 3 =
1+ 32 = x ,1+ 2 34 = y3 = yx= yx
) (1+ 2 34 ) (1+ 323) (1 + 3) (32 = 1+2 = 3 =
1+ 32 = x ,1+ 2 34 = y3 = yx= yx
) (1+ 2 34 ) (1+ 323) (1 + 3) (32 = 1+2 = 3 =
-
48
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xa
.
a , x xa
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a = )x( f R x }1{ /+R a x
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(
h ( x) 5 ( = )x(
12
:
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1 = a
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x) ( = )x( f
-
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.
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.
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12
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x
x
x
x
x
x
x
x
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o
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13
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a
a
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78
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: 441 4 84 741 3
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3 /
:
4 /
:
(
(
(
( x
5 /
:
(
6 / : .
172
8119
: snA
72 + 2- 4 6 : snA
16
12
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3 2
x2b - a
3x81
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1 - 5
51 -x + 6 - x
542
) + 3 ( 2
: snA
32
8 - 72
32 - x
3 0 = - + 3+ x
1 - 5 1 + 5 -
1 + 5
5
19
34
3b - a
b - a: snAx
13
1 : snA
b3 +a8 = x3 +x
1 = y5
x
b3 +a8 = x3 +x
1 = y5
x
-
888888
Gd GdGH : M Gd 4 ]1-4[
]2-4[
]3-4[
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x x niS x x soC x x naT
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-
98
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. .
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: = r
r: a : b : x :
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:
soC niS2= x niS
x2niS y2niS - y2niS + yniS x2niS- x2niS =)y+x(niS
= xtoC = xnaT
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)998 ( = ) 2941(
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56859717581382.6
:
....(
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.
x soC bx soC - a
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x2
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= 2
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r . Q =L
1 4[ yrtemonogirT
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>
A
C
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Y
XX
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Y
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XX
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erusaeM eergeD : :
063 063
1
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erusaeM naidaR :
.
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crA .
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= r r = L B O A
= 1 .
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| Q | .
= = | Q |
A
B
L
o rr
B
L
r
o
r
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3 - )
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4 - )
Lr
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A
r . Q =L
-
29
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= r2
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2 = 063
= 081
1 =
1 = .
: ( = Q
Q =
( = D :
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: =
.
Lr
r2r
081
081
D081
081QD
081
2 = = | Q |
Q
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39
1
B O A mc01
mc21 .
( B O A :
.
( B O A m :
mc 21 = r mc 01 = L
( 338 .0 = = = = | Q |
( :
338 .0 = = = = | Q |
338 .0 - = Q ) (.
2
B O A
=
= 081 = D =
Lr
0121
56
0121
56
34
QD
081
3 4
D34
-
49
3
: ( 54 .
( 6.2 .
( = = Q = .
( = = = 081 6.2 = 864
4
06 9
= = Q = .
=|Q|
QD
081
081
Q 54
4
QD
081
081
6.2
D
QD
081
Q06
081
13
Lr
D
241.3 3 = 3
mc 624.9 =
L9
= = L 3
-
59
Lr
7161
41 1202
QD
081
7161D
081
7161
14
1 . . . . . . . 09 = B + A2 . . . . . . 2.52 = B - A
2.511 = A 2 6.75 = A
4.23 = B
722
081
QD
081
= D
44.0D
081 44.0
081 44.041.3
2.52= =
mc mc
5
12 02
|Q|= |Q|= = .
= =
58 .06 = 081 =D 6
44.0
= =
B A
-
69
) 1 - 4 (
1 /
:
03 021 003
2 /
:
3 /
52
. / 03
4 /
531 8
/ 758.81
5 /
9
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6 /
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56
13
56
4
5>BOA 4
mc
mc
mc
mc
-
79
4 4[
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2. ) enisoC ( )Q(
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C B
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Q
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.PPO .PYH
CACB
CBA
Q = CBA < m
CA = = Q niSBA
CBBA
.JDA .PYH
CB = = Q soCBA
.PPO .JDA
= = Q natCACB
-
89
BA
BA
2)BA( = 2)CB(+2)CA(
2)BA(
2
1 = Q 2soC + Q 2niS
CA = Q natCB
= Q natCB BA
CA BA
= Q natQ niS
Q soC
CA
BA
CB
BA
) 5 - 4(: ) (
:
= +
) 4 - 4 (
:
)4-4( :
) BA ( :
2 2
-
99
5 4[ oitaR cirtemonogirT
1 ( 54
CBA B . )54( )54(
L = CB = BA
:
2L2 = 2L+2L = 2)CA(
2 ( 03 06
= L2
= 06
CBDA
L = BD = DC
03 = DAB m
=
(
A
B C54
54
L
L
L
A
06 BCL
L2
L
06L
03 03
L2
D
2)CB( + 2)BA( = 2)CA(
L 2 = CA
L =54 niS = = 54 niSL2
12
12
L =54 soC = =54 soCL2
12
12
L1 = 54 nat = =54 nat L
1
L 3 DA
L =03 niS = = 03 niSL2
12
12
L3L2
3 =06 nis = = 06 nis2
2
3
L
-
001
:
.
Q
) ( :
:
: 03 , 06
03 + 06 = 09
L3 =03 soC = =03 soCL2
32
32
L =06 soC = =06 soCL2
12
12
L =03 nat = = 03 natL3
13
13
L3 =06 nat = = 06 natL
331 = 03 nis
2 = 06 soc
32
= 06 nis = 03 soc
Q soc = ) Q- 09( nis
Q nis = ) Q- 09( soc
Q - 09
-
101
6 4 [
)5 - 4(
: .
Q = A O B m
B
nis = Q nis
soc = Q soc
)6 - 4(
tnioP cirtemonogirT
.
y1
A y
Ox
y
) y,x(B
x
:
: Q nis = ) Q-081( nis Q soc- = ) Q-081( soc Q nat- = ) Q-081( nat
x1
)Q nis,Qsoc( = )y,x(B
B O )y,x(B
Q
Y =Q
X =Q
-
201
B BOA Q
)y , x( = = x .
7
Q nat
0 09 081 .
) 6 - 4 ( :
0 = 0nat = = 0 nat
) 0,1( = ) 09 nis , 09 soc( 1=09 nis 0 =09 soc
09nat=
)0 ,1- ( = )081 nis , 081 soc( 0 =081 nis 1- =081 soc
0 =081 nat
)6 - 4(
0nis0soc
01
09nis09soc
(
Q socQ nis y
081 09 0 = Q Q nisQ soc
1 = 0 soc )0 , 1( = )0 nis , 0 soc(
0 = 0 nis
)0,1-( c
Y
X )0nis , 0soc(
)09nis ,09soc(
O
A
0=
)1-,0( D
)0,1(
)1,0( B
-
301
4 7[
]1-7-4[ : .
A C A
C A ) C noitavelE fo elgnA
A( BAC )7 - 4(.
C
A C
A C )
A noisserpeD fo elgnA
C (
D C A ) 7 - 4( . )7 - 4(
8
03 ) (
54 .
= L
C B A B .
)8 - 4(
A
A D
A
C
B
A
03
B C54
L
12
.PPO.pyH
L= = 54 nis03
032
m12.12 = =L
-
401
C
9
8 06
B : =06 nat
= 3
8 3 = .
)9 - 4(
01
0532 07
6939.0 = 7 nis.
=
CBA B
= 07 nis
= 6939.0
)01 - 4(
BAC8
A
06B
BACA
0532CA
.PPO.pyH
BA
C B A
)
A
B07
C
07
253
0
05326939.0
m0052 = CA
-
501
11
7 06
03 .
B CA = CAD
] = [
CBA B :
= 03 nat
. )11 - 4(
D A E D : = 06 nat
12 = X = 3
= 7 +X
=7+12= 82
7Y
13
7Y
X7 3
XY
A
C
E
X
D
7
06Y03
Y03 B
7
3 7 = Y =
-
601
D
xy
21
03
0001 54 .
CBA B :
=54nat
= 1
1 . . . . . y = x
. . . . . = 03 nat
0001 + y = y 3
0001 = y - y 7.1
= y
6.8241 = x .
x0001 + y
13
D
= 03 nat
y0001 + y
00017.0
A
BC
X
03Y0001
54
54
xy
2
= )21 - 4 (
6.8241 =
-
701
]2-7-4[ rotceS ralucriC :
)7 - 4(
.
)31-4( BOA elgnA lartneC
081.
= BA
= . . . . . 1
= Q
Q = r Q = L
1 :
= . . . . . 2 ) 31 - 4 (
1 : =
2 : = =
= D .
= =
=
12
12
Lr
12
BA
C
O
rrQ
L
1rQ 2
2
2r
Q 2
Q 2
D063
Q 2
D063
063
:
L + r + r =L + r 2 = L r
.
)r L
2 r Q
21r ) 2 ( 2
2 r = 2
r
-
801
31
06 8 .
= 2r Q
= 46
= 46
: =
= 46
= 41. 3 46 = 94 . 33 2mc .
41
51 2mc mc6
.
1 - = r L
2 - = L 2 + r
5 2 + 6 = 61
3 - | Q | = Q = = 2.1
= =
D = = 8986 . 86
12
12
06 081
12
41.33
D06306063
16
12
12
Lr
65
QD
081
2.1D
41.3081
2.1 08141.3
2mc 94.33
5= r r 6 = 51
mc
-
901
]4-7-3[ tnemgeS ralucriC :
)8 - 4(
.
BOA )41 - 4(
081
:
)41 -4(
Q
BCA = )BCAO ( - BAO
) BCAO( = 2r Q
BAO = Q nis BO AO
BAO = Q nis r r
CA = Q nis 2r -
Q r .
12
)
)
12
12
12
12
12
B A
C
O
rrQ
BCA = )Q nis - Q( 2r
2r Q
-
011
51
21 mc 03.
= = 6325.0 = Q
=
= ) 5.0- 6325.0 ( 441
= )6320.0( 441 = 7.1 2 mc
61
O 6 mc 6 mc 2mc
.
BOA )51 -4(
= = Q = = = 740.1
=
=
= )568.0- 740.1 ( 81
= )281.0( 81 = 672.3 2mc
081
12
QD
Q03
12
12
081
081
QD
081
Q06
3
2212
12
= = = 740.1
B
O
mc606
mc6
)03 nis - Q ( 2 r
06 = BOA m
12
)Qnis - Q( 2r
63
A
) 06nis-740.1(
-
111
) 2 - 4 (
1 /
07 05
03 2.1 = 05 nat 8 .2 = 07 nat
/82 . 41
2 /
)05( 03
/ 9. 82
3 /
mc8 mc2.3
/2mc8.21
4 /
001 mc01
/ 2mc3.38
5 /
2mc86.73 mc6
/ mc65.21
6 /
mc01. 54
/ 2mc89.3
7 /
06 mc8
/ 2mc18.5
-
211
84[
]2-4[ :
GED
)EERGED(.
DAR ) NAIDAR( .
GRD GED DAR .
.
nis )enis(.
soc )enisoc(.
nat )tnegnat(.
)GED( )DAR( )GRD( .
.
.
:
71
)1( * : GED .
* 03.
* )nis( = 5.0 .
1.
2.
3.
:
053 nat )3( 021 soc )2( 03 nis )1(
Q nis - = )Q (nis
Q soc = )Q -( soc
Q nat - = )Q -( nat
-
311
)2( * : GED
* 021.
* )soc( = 5.0
)3( * : GED
* 053 )nat( ~ 3671 . 0
) ( )) ((.
81
: DAR fdn2
) . . . ( .
: = )1(
* DAR
* fdn2 456295141.3 5 = 72369707.51 4 = 718099629.3 187601707.0 -
)2(
Q soc = )Q - (soc ) (.
* DAR.
* fdn2 = 456295141.3 3= 169777424 .9
soc
= 1 -
-
-
3671.0 - ~ 053 - nat
54
7)1( nis )2( 5
3 - soc )3( nat
54
nis
nis =
3 - soc
Q nat - = ) Q - ( nat
VNI
-
411
)3(
* DAR.
* fdn2 = 456295141.3 7 = 8584119. 12
5 = 517922893. 4 = 73536770.3 .
:
)1( )2( )004-(
)1( 5.0
)2( 344440667.0
)3( 291949762.0 -
)4( 885.0 -
)5( 5.0 -
)6( 735386770.3-
6
75
nat
nat
)4( ) 63-( nat)3( ) 51-( natsocnis2 )5( soc3
85
)6( nat
-
511
94[ elgnairT delgnA thgiR fo noituloS
] [
.
91
4 .0 = 22 nat :
)1( 22 soc 22 nis
)2( 86 nis 86 soc
= = = = 22 nat
= k2
= k5
. . . . . .
2K92 = 2K52 + 2K4
K 92 = CA
)1( = = = = 22
= = =22
)2( = 22 = )22- 09( = 86
25
401
CBCA
BACA
2) CA (= 2) CB ( + 2) BA (
k2k92
k5k92
292
592
nis
soc
nissoc
BK 5
C
A
86
22
K 2
nis
2 =22 nis = )22 - 09 (soc = 86 soc92
k 92
592
-
611
02
= C soc CBA B. ,Anis C nat
Asoc
CBA B :
= = C soc
)(
52 + 2)BA( = 2 K
K21 = BA 2 K 441 =2)BA(
= = C nat
= = Asoc
12
CBA A mc 42 = CA mc 7 = BA :
B soc C nat B nis C nis
2)C A(+ 2)B A (= 2) CB (
526 = 675 + 94 = 2 )42(+ 2 )7( =2) C B(
mc 52 = CB
531
k5k31
k21k5
215
k21k31
2131
2 )CB( + 2)BA( = 2 )CA(
961
C
A
B
K21K31
K5
k5k31
5 31
=A nis
=
C
B
A
mc52
mc42
mc7
-
711
= B nis = C nis
= B soc =C nat
22
CBA B . mc 3 = BA mc 6 = CA
2)CB( + 2)BA( = 2)CA(
2)CB( + 9 = 63
3 3 = CB
= = C nat
06 = 03 - 09 = A< m
752742
4252752
303 = C3 3
13
A
C
mc 6
mc3
mc 3 3
06
B 03
-
811
) 3 - 4 (
1 /CBA B = C nis : A nis C nat C soc .
2 /C BA C mc 42 = C B mc 52 = B A
B 2soc + B 2nis . 3 /
= Q soc Q nat Q nis 4 /
01 03
) 37 .1= 3 ( :snA 5 /
C B A C 06 = B A C
-
911911911
Gd Gde : Gd srotceV 5 ]1-5[
]2-5[
]3-5[
]4-5[
]5-5[
a )y , x( = a
a 2 y + 2 x = a
* ) 0 , 0( = 0u
1u , ) 0 , 1( =
2u ) 1 , 0 ( =
1u ,
2
-
021
: srotceV
15[ )) ((
.
.
A B
B A
A B a ) (
:-
)1(
)2(
.
aB A
-
121
:
FE DC BA .
) 1 - 5 (
. )2-5( B A D C
B A F E
) 2 - 5 (
D FB
EC
F
B D E
A C
A
-
221
25[ rotceV lacilronoC
)0 , 0(
. )
(.
:
E O F O
B A D C
) 3 - 5 (
]1-2-5[ :
)3 , 4(
)3 , 5( )2 , 3( C B
.
AO BO CO
) 5 - 4 (
YD
C
B
F A
X
E
O
Y
X
)4,3(A
)2,3(C)3,5(B
O
-
321
)3,4( )5,3( )3,2( .
:
.
) 5 - 5 (
35[
]1-3-5[ :
.
BA BA || BA || .
) 5 - 6 (
)1-5(
A :
2y + 2x = A O= || A || = AO
)6 - 5(
)y , x( = A = AO
)y,x( = A
Y
X
)y,x(A
L
)0,0(O
Y
X
)y,x(A
Y
X)0,0(O
A
-
421
1
:
)4,3( ) , ( ) 9- , 21- (
)4,3( :
) , ( :
) 9- , 21- ( :
)2-5(
rotceV oreZ : )0,0(
. 0 0 = || 0 || = .
)3-5(
x( 1y ,
1x( )
2y,
2 : )
x.1x =
2y
1y =
2
)4-5(
: .
2 701
201
5 = 61 + 9 = 2) 4 ( + 2) 3 (
21 = = + = 2)( + 2)(01
2 7 01
2001
89001
001001
2 701
201
51 = 522 = 18 + 441 = 2)9-( + 2)21-(
-
521
]2-3-5[ :
A Q
A
.
= Q nis , =Q soc
2
2 = 1 + 3 = 2) 1- ( + 2) 3 ( = || BO ||
Q
BO
)7-5( Q
: = - 2
) 7 - 5 (
2 < Q 0 )y , x( = A
x2y +2x
y2y +2x
)1- , 3 ( = BO
= Q soc
= Q nis
32
1-2
11 66
Y
XQ
O3
)1- , 3 ( B
-
621
3
) , (
Q ) , (
)8 - 5(
= = Q soc
= = Q nis
)8-5(:
Q
12
12
12
12
12
12
12
12
2) ( + 2) (
12
12
2) ( + 2) (
4
y
X
12
12
540
1122
12
12
1 (2
12
(
12
12
-
721
4
= 5
= ) y , x (
= = soc = Q soc
= x
= = nis = Q nis
= y
) , (
6
a
xa
6
x5
x5
32
3 52
ya
6
y5
12
y5
55 2
23 5
2
-
821
) 1 - 5 (
1 /
:
( )2 , 2- ( ( )0 , 3-( ( ) 3 , 1(
( ) 6 , 0( ( ) 1- , 3 ( ( ) 3- , 3- ( ( )8- , 0 (
2 /
:
= Q 2 = || B || )
= Q 2 = || B || )
= Q 4 = || B || )
= Q 3 = || B || )
= Q 4 = || B || )
4
6
3
2
2
3
-
921
45[
]1-4-5[ :
B A
)9-5(
) 01 - 5 ( .
)9-5( )01-5(
A
C B A ) 11 - 5 ( .
)11-5(
) y , x (
c
O
)y- , x-( B
X
YA
AA
B
A
AB
BA
B +
B
+
-
031
B A
A A- .
)5-5(
:
x( = B + A 1y ,
1x( + )
2y ,
2x( = )
1x +
2y ,
1y +
2)
5
B + A
)5 , 4( = )4 , 1( + )1, 3( = B + A
)21 - 5(
B + A B A
2y+2x = || B || = || A ||
)y- , x-( = B )y ,x( = A
x( = A 1y,
1x( = B )
2y ,
2 )
)4 ,1( = B )1 , 3( = A
Y
X
)4,5(
)1,4(B
)3,1(A
)0,0(O
B
A
+AB
)21 - 5(
-
131
6
B + A .
)1, 1( = )2- ,5 ( + )3 ,4-( = B +A
245[
)1( : B A B + A .
)2( : C B A
)C+ B( + A = C + )B + A(
)3( : B A A+ B = B + A
)4( :
: A A = A + )0,0( = )0,0( +A
)5( : A B-
)6( : B A C +A = B + A C = B
7
)3 ,2-(
)3 , 2-( )2 , 3- ( :
)0 , 0( = ))3- (+3 ,2 + 2-( = )3- , 2( + ) 3 , 2- (
)0,0( = A + )B-( = )B-( + A
)2- ,5 ( = B )3 , 4-( =A
-
231
345[
)6 - 5(
K
:
A A K || A || K
A 0 > K A .
)31 - 5( 0 < K )( A K A
K || A || .
K A A .
)31 - 5(
) y K , x K ( = K A = A K )y , x( = A
) y , x ( = A
xKyK
yK
X
Y
xK
yX
xK()yK,
X()y,
0 > k
0 < k
,
-
331
8
C3- C C2
) 2- , 6( = )1-,3(2 = C2 ) , ( = )1-,3( = C
)3,9-( = )1- , 3( 3- = C3-
9
2- = L 3 = K
)1 , 7( = )3 + 2- , 4 + 3 ( = B +A )1()6- , 9( = )2- , 3( 3 = A K )2() 6- , 8- ( = )3 , 4( 2- = B L)3() 6- , 8- ( + )6 - , 9( = B L + A K )4()21- , 1( =
445[
)1( : B A K :B K +A K = )B +A ( K
)2( : A R L K :
)A K( L = )A L ( K = A )L K(
21)3 ,1-( = C
32
12
1-2
)3 , 4( = B )2- , 3( = A B L + A K )4( B L )3( A L )2( B + A )1(
K B + K A = K )B + A (
12
-
431
10
)3( : B A R K K B K = A K B =A .
)4( A = 1 A = A )5( 0 = 0 A = A
545[
)7 - 5( B A B - A
01
B - A
)1 , 4 ( = )3- , 1( + )4 , 3( = )B-( + A = B - A :
: B - A A B.
)41 - 5(
B.
)B -( + A
)3 , 1-( = B )4 , 3( = A
)4, 3(
)1, 4(
)3-, 1(
)3, 1-(
A B
B-A
B
X
Y
-
-
531
11
)1( B L - A K ) 2 ( B - A
)1- , 2-(-)3 , 2( = B - A )1(
)4 , 4(=)1 , 2(+)3 , 2( =
)51 -5( :
) 51 - 5 (
)1-,2-()1-( - )3, 2( 2 = B L -A K )2(
)1 -,2-( + )6 , 4( =
)5 , 2( =
:
) 61 - 5 (
A A B B -
B = B - 1-
B B +A
.
1- = L 2 = K )1- , 2-( = B )3 , 2( = A
2
2
Y
X
)4, 4()3, 2(
)1, 2(
)1- , 2-(
A
B
)6, 4(
)5, 2(
Y
XB
)1-, 2-(
KKA
- AB L
-
631
55[
1 5 5 [ rotceV tinU
)8 - 5(
U 1)1(
.
U 2)2(
.
:
)y , 0( + )0 , x( = C
)1 , 0 ( y + )0 , 1( x = C
U 1 U
2
U x = C C
1 U y +
2
U : 1U
2 )9 , 0 ( )3- , 0( )0 , 2-( )0 , 6(
U9 1U3- = )0 , 3-(
1U2- = )2-, 0(
2 U 6 = )6 , 0(
2
21
B + A .
U - = )1 , 0(01 + ) 0 ,1(- = ) 01 ,1- ( = ) 3 , 5- ( + ) 7 , 4 ( = B + A 1 U 01 +
2
U 1) 0 , 1( =
U 2 )1 , 0( =
)y , x( = C
)3 , 5-( = B )7 , 4( = A
=)9,0(
-
731
U :1 U
2
U2 = )5 ,2(1U5 +
2
U 4- = )2 ,4-(1 U2 +
2
U 2- = ) 3- , 2- ( 1U3 -
2
U 4 = A 1U5 +
2
U2 -=B .1U3 +
2
31
U = A B +A1U3 -
2U2 = B
1U +
2
U ( = B +A1U3 -
2U2( + )
1U +
2U = )
1U + )2+1(
2U3 = )1 + 3-(
1U2 -
2
41
3 = L 2 =K B L - A K
.
)4 ,3-( 3 - )3- ,5( 2 = B L - A K
)21- , 9( + )6-,01( =
)81-, 91( =
U 91 = 1U 81 -
2
)5,4( = A
)3 , -2( = B
)4,3-( = B )3- , 5( = A
)2-,3(=
-
831
) 2 - 5 (
1 / :
U 3 )0 ,3( )2- , 2-( 1U +
2U-
1U2 -
2
2 / :
U3(7 )5 , 1-(4 +) 1-,2( 3 )5,1(7- )1- , 1(2 )1-, 1(4 1U2 +
2U2(4- )
1U-
2
3 /U:
1U
2
)3 , 2( )0 , 2( )3 , 5 ( )1- , 0( )5- , 3-( )4, 1-(
4 / R y x A
A = A + E = E + A
5 / B- = A
6 / 2- = L 3 = K )3 , 2 ( = B )1 , 3 ( = A
:
7 /U
1U
2 6
8 /U
1U
2
) ( 3 )( 01
)( 5 ) (
9 / x : B5 = x3 + A2 .
)0 , 0( = E
B L + A K B - A K B + A K B+ A A L B K
)B + A( )K + L( A )K + L( )B + A( K B L - A K
)B - A ( L K )B K + A L( K
)0,0( = A + B = B + A
)4-, 2( = B )2 , 5( = A
)x , y( = E
34
34
6
)
-
931931931
Gd GdOS : GdS GMGK 6 ]1-6[ .
]2-6[ .
]3-6[ ) ( .
]4-6[ .
]5-6[
]6-6[ .
]7-6[ .
]8-6[ .
n1
n2
n1x
2n+
2x
1n
1n+
2
n1y
2n+
2y
1n
1n+
2
xa|1yb +
1|c+
2b+2a
x( = L
x-
1y( + 2)
2y_
1 2)
) , (
m L // L1m =
2L
1L,
2
L 1
L 2
m1m
2L 1- =
1L,
2
0 = c + yb + xa
D = D
-
041
: : yertemoeG citylanA
16[
y y x x )O(
)R( O
X X y y
A
C A B A )1 - 6(
.
.
)1 - 6 (
)2 , 3 ( A
Y
X
)2,3 (A)2, 0 (C
)0, 3 (B )0, 0 (O
-
141
2 6[ stnioP woT neewteB ecnatsiD
:
:
C B A: C
+ = 2L ............
x ( = L 2x -
1y(+2 )
2y -
1 2)
.
:
A- B = B A
x( = B A 2y ,
2x ( - )
1y ,
1)
x( = )2 - 6(2x-
1y
2y -
1 )
..
1
.
:
)3- , 1-( = )7 ,2-( - )4 , 3-( = A- B = B A
)3-, 1-( 3- = )9 , 3( = )7 , 2-( - )61 , 1( = A- C = CA
B A3- = C A
C B A .
:
............
)61 ,1( C )4 ,3-( B )7 , 2-( A
x ( =|| B A ||2x -
1y(+2 )
2y -
1 2)
x( A1y ,
1x ( B )
2y ,
2 )
2)CB ( 2)CA( =
x (B2y,
2)
L
x (A1y,
1)
y 2y-
1
x 2x-
C 1
O
y
x
-
241
:
01 = 9 + 1 = 2) 4 - 7 ( + 2) 3 + 2- ( = BA
01 4 = 061 = 441 + 61 = 2) 61 - 4 ( + 2) 1 - 3- ( = CB
01 3 = 09 = 18+ 9 = 2)61-7( + 2)1-2- ( = CA
CA + BA = CB
C B A
.
2
2 = 1+1 = 2)1-2(+2)1 -2 ( = BA
02 = 4+61 = 2)1-1-(+2)1 -5 ( = CA
81 = 9+9 = 2)2-1-(+2)2 -5 ( = CB
2CB + 2BA = 2CA : 2 ) 81 ( + 2 ) 2 ( = 2 ) 02 (
81 + 2 = 02
CBA B .
)1- , 5( C )2 , 2( B )1 , 1( A
-
341
3
.
5= 52 = 9 + 61 = 2) 4 + 1- ( + 2) 1- 3- ( = BA
28 = 1+ 18 = 2 ) 5 + 4- ( + 2) 01- 1 ( =CB
5= 52 = 9 + 61 = 2) 2 + 5- ( + 2) 6 - 01 ( = DC
28 = 1 + 18 = 2) 1+ 2-( + 2) 3 + 6 ( = DA
DA = CB DC = BA
DCBA ) (.
4
)CA=BA ( R a .
CA=BA
) (
)2- , 6( D )5- ,01( C )4- , 1( B )1- ,3-(A
)a2 ,3( A )1,a( B )1 ,4(C
B
A
C
2) (1 a2 + 2) (4 3 = 2) (1 a2 + 2) (a 3
2) (1 a2 +1= 2) (1 a2 + 2) (a 3
1= 2) (a 3 1 = a 3 2 = a 1= a 3 : 4 = a 1 = a 3 :
-
441
) 1 - 6 (
1 /
:
( )4 , 3( )0 , 0(. ( )4 , 6( )2 , 1( .
( )5 - , 3- ( ) 1- , 5 ( ( )4 , 1-( )3 , 2-(.
2 /
)8- , 3-( C )01 ,1 (B )7 , 5(A.
3 /
.
4 /
)9-, 8( D )7- , 0( C )0 , 5- ( B )2- , 3( A
.
5 /
DCBA
D.
6 /
.
7 /
)0 , 0( )8 , 6( )4- , 3-( .
)4- , 3( C )1- , 1-( B )3 , 2( A
)2 , 4-( C )3 , 3( B )5 , 2-(A
)5- , 1-( D )2, 8-( C )01 , 7 (B )3- , 4(A
-
541
]3-6[ ) ( :
.
C B A
n : 1n :
2
=
= Y = = X
C ) , (
4
1 = = = = x
2- = = = = y
)2- , 1 (
X = = X = = X
x( = A1y ,
1x( = B )
2y ,
2)
)y , x( = C
n1x
2n+
2x
1n
1n+
2
n1y
2n+
2y
1n
1n+
2
n1
n2
CABC
n1x
2n+
2x
1n
1n+
2
n1y
2n+
2y
1n
1n+
2
12
)0 ,5-( B ) 3- , 4( A
)4(2+)5-( 12+1
n1x
2n+
2x
1n
1n+
2
n1y
2n+
2y
1n
1n+
2
)3-(2+)0( 12+1
6-3
8+5-3
2 x(B )2 y,
x(C)y,
1 x(A )1 y,
n2
n1
-
641
:
M BA
) , ( = M
n .1n =
2 n =
5
C BA
C
) , ( = C
) , ( =
) 3- , 2 ( = C
x1x+
22
)8- , 7( B )2 , 3-(A
x ( A1y ,
1 x( ( B )
2y ,
2)
y1y+
22
x1x+
22
y1y+
22
)8-( + 2 2
7+3-2
-
741
)3- ,1( B )1 , 2( A
) 2 - 6 (
1 /
B A
.
2 /
BA .
3 /
C BA
4 /
C A B
)4- , 4( B
5 /
C B A :
.
6 /
)8- , 5-( ) 3- , 3- ( )3 , 1( )2-, 1-(
.
)3- , 2( C )2 , 5( B )0 , 4(A
)6- , 3-( B )4- , 2( A
)6 , 4( B )3 , 1( A
)6 , 2(A
21
35
-
841
4 6[ eniL ehT fo epolS
)1 - 6(
x( B 2y ,
2x ( A )
1y ,
1 )
. x
1x
2 BA =
:
y BA = 2y -
11( 0 =
BA // .
= = .
x BA 2x -
12( 0 =
BA // .
= .
3( Q BA
Qnat } 09 { / ) 081 , 0 [ Q .
6
)1 , 5( B )3 , 2( A
= = = BA polS
y2y -
1x
2x -
1
y2y -
1
x2x -
1
3 - 1 2 - 5
2 - 3
BA
-
941
5 6[ noitidnoC lellaraP
. m
1m =
2L
1L //
2
7
) 0 , 1( C )1 , 2( B )3 , 4(A .
= = = BA m
= = = CB m
CBm = BA m
A B C .
6 6[ noitidnoC ralucidnepreP
L 1L
2 = 1-
m
1m
2 1- =
m
1 =
=
= .
1
1
2 - 2 -
1 - 1 -
3 - 14 - 2
3 - 02 - 1
1 - m
2 3 -
4 4 3 -
3 4
-
051
8
)11 , 5( C )4 ,01( B )1- , 3( A
B
= = CBm , = = BAm
1- = = CBm BAm
CB BA
CBA B .
9
)b , o( A )2 ,1-( B )4-b , 2-( C
R b .
C,B,A
:
)1-( - 401 - 5
53 - 01 7
7 4 - 11 5-
7 7 5
5-
CBm= BAm
b2 = o1
2 ) (4 b12
b2= 1
6 b6b =b2 1
4 =b yV =m
xV
CBm= BAm
b2 = o1
2 ) (4 b12
b2= 1
6 b6b =b2 1
4 =b yV =m
xV
-
151
) 3 - 6 (
1 /
)1( ) 0 , 2( )2- , 0(.
)2( )6 , 7- ( )4 , 1-( , )3 , 2( .
)3( ) h , 3- ( B )3 , 2(A h = BA
)2- , 7( C )8- , 2-( B )6 , 1(A
)4( CBA
CBA B .
2 /
:
1( H L H )3 , 2( )5 , 1( L
( ( 2- ( (
2( H L H )2- , 3( )2 , 3- ( L
( ( - ( (
3( L )5 , 1-( )3 , 1-( H )6 , x( )4 , 3(
x ( 3- ( 3 ( 1 ( .
1 2
1 2
2 3 3
2 -
3 2
2 3 3
3- 2 - 2
H L
M
-
251
3 /
1( )2- , 2( C )1 , 2-( B )2 ,5(A .
2( )2 , 0(D )2-, 6( C )1 , 5( B )5 ,1-(A DCBA .
3( )4 , 2( D )1 , 0( C )1-, 3( B )2 , 5(A DCBA .
4( CBA )3- , 2-( C )0 , 6( B )4 , 2( A :
( A CB .
( B CA .
5( ) 4 , 2( D )2 , 4( C )2- , 2( B )2 , 2-( A
.
6( x )9- , 2-( )4 , x(
)3 , 0( )1 , 4(.
7( :
.
R a2 = y+) (1+a : 2 L6+xa = y2: 1L
R a2 = y+) (1+a : 2 L6+xa = y2: 1L
R a2 = y+) (1+a : 2 L6+xa = y2: 1L
-
351
76[ eniL ehT fo noitauqE
)y , x ( y x
.
: 0 = c + y b + x a
1. 0 = x
= y
0 = y = x
2. 0 = b 0 = c + xa 0 = x .
3. 0 = a 0 = c + y b
0 = y .
4. 0 = c 0 = yb + xa .
1. :
x( A :1y ,
1x( B )
2y ,
2 BA )
BA ) y , x( C :
= .
2. :
= m
y y . . . . . . . . . . . . . .1x x( m =
1 )
c- b
c- a
y - y1
x - x1
y2y -
1
x2x -
1
y2y -
1
x2x -
1
-
451
9
)5 , 4( )3- , 2(.
=
=
=
8 - x4 =
0 = 11 y x4 ......... .
01
)3,0( )1,7( )4 , 3(
= =
7 + y7- = 41- x2
0 = 12 y7 + x2 ....... .
)4 ,3( 4 = y 3 = x .
0 = 12 - ) 4 (7 + )3 (2
0 = 12 - 82 + 6
3 + y 2 - x
y - y1
x - x1
y2y -
1
x2x -
1
2 - 43 + 5
1 3 + y 4
2 - x
7-1 - 3 2
7 - 0 1 - y 7 - x
3+y
??
) 5,4(
Y
X
)3- ,2(
)4,3(
Y
X
-
551
0 31
)4 ,3( .
11
)3- , 1( .
y - y1x - x( m =
1 )
) 1 - x( = 3 + y
1 - x = 6 + y2
0 = 7 - y 2 - x . . . . . . . . .
21
) 5 , 2-(A ) 3, 2-( C )1- ,4( B .
D C B = ) , ( = D
DA : =
8 - x4- = 51 y3
0 = 7 y 3 + x4 . . . . . . . . .
. . . . . . . . .
= ) , ( = D
2
1 2
1 2
5 - 1
3 + 1- 2
)1,1( )2-( + 4
2 + 1 5 - y 2 + x
Y
X
) 3-, 1(