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222 2 bababa

))((22 bababa

abb)x(axb)a)(x(x 2

abbaba 2)( 222

abbaba 2)( 222

abbaba 4)()( 22

abbaba 4)()( 22

2222 )()()(2 bababa

22 )()(4 babaab

, 22

22

babaab

yx 53 : 222 55323)53( yyxxyx = 22 25309 yxyx

25 : (25)2 = (20 + 5)2 = (20)2 + 2205 + (5)2 = 400 + 200 + 25 = 625

4x 7y :

222 77424)74( yyxxyx 22 495616 yxyx



8 ba 15ab , 22 ba :

abbaba 2222 1528 2 3064 34

7 ba 60ab , 22 ba :

abbaba 2222 6027 2 12049 169

3 yx 10xy , 2yx :

xyyxyx 422 1043 2 409 49

7 ba 10ab , 2ba :

abbaba 422 1047 2 4049 9

51

xx ,

21

xx

:

xx

xx

xx 1411

22



45 2 425 29

ba 52 :

222 55222)52( bbaaba 22 25204 baba

74 x :

222 77424)74( xxx 495616 2 xx

7 ba 9ab , 22 ba :

abbaba 2222 927 2 1849 31

5 yx 6xy , 2yx :

xyyxyx 422 645 2 2425

49

: ba 52

74 x

7 ba 9ab , 22 ba

5 yx 6xy , 2yx



43 p 43 p : 4343 pp 22 43 p 169 2 p

85 m 95 m : , abxbaxbxax )(2 9585 mm 9859825 2 mm 7251725 2 mm 728525 2 mm

: 22 494975275 ababbaba : , xba 75 yab 49

22 2 yxyx 2yx 24975 abba [x y ] 22ba

22 44 baba

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: yx 75 yx 75 10x 14x yx 34 yx 56



yx 75 yx 75 : yxyx 7575 22 75 yx 22 4925 yx

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xzyzxyzyxzyx 2030122594534 2222

cba 765 :

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2)}76()5{( cba

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222 498436706025 cbcbacaba acbcabcba 708460493625 222

:

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2222 )7()6()25()765( cbacba )5()7(2)7()6(2)6()5(2 accbba acbcabcba 708460493625 222

[a, b, c ]

: : cbyax zyx 754



cbyax :

)(2)(2)()(2)()()( 2222 axccbybyaxcbyaxcbyax

acxbcyabxycybxa 22222222

. zyx 754 :

)7)(4(2)7)(5(2)5)(4(2)7()5()4()754( 2222 zxzyyxzyxzyx

xzyzxyzyx 567040492516 222

. :

() ba 75 () 36 x () qp 27 () byax () xyx 3 () ba 1211 ()

22 56 xyyx () yx () abcxyz ()

4232 ybxa () 108 () 606 () 597 () cba () 2 bax () zxyzxy () rqp 523 () 222 zyx

() ba 75 :

ba 75 2)75( ba

22 )7()7()5(2)5( bbaa 22 497025 baba

() 36 x :

36 x 2)36( x

22 )3()3()6(2)6( xx 93636 2 xx



() qp 27 :

qp 27 2)27( qp

22 )2()2()7(2)7( qqpp 22 42849 qpqp

() xyx 3 :

xyx 3 23 )( xyx

2323 )()()(2)( xyxyxx 2246 2 yxyxx

() 22 56 xyyx

: 22 56 xyyx

222 )56( xyyx 222222 )5()5()6(2)6( xyxyyxyx

423324 256036 yxyxyx () acbxyz

: abcxyz

2)( abcxyz 2)}({ abcxyz

2)( abcxyz 22 )()()(2)( abcabcxyzxyz

222222 2 cbaxyzabczyx

() byax :

byax 2)( byax

22 )()()(2)( bybyaxax 2222 2 ybabxyxa

() ba 1211

: ba 1211

2)1211( ba 22 )12()12()11(2)11( bbaa

22 144264121 baba () yx

: yx

2)( yx 2)}({ yx

2)( yx 22 2 yxyy

() 4232 ybxa

: 4232 ybxa

24232 )( ybxa 2424232232 )()()(2)( ybybxaxa

84432264 2 ybyxbaxa



() 108 : 108

2)108( 2)8100(

22 )8()8()100(2)100( 64160010000

11664 () 597

: 597

2)597( 2)3600(

22 )3()3()600(2)600( 936000360000

3600360009 356409

() 2 bax

: 2 bax

2)2( bax 2}2){( bax

22 )2()2()(2)( baxbax 4442 222 baxbabxxa 4442222 axbabxbxa

() 606 :

606 2)606(

2)6600( 22 )6()6()600(2)600(

367200360000 367236

() cba

: cba

2)( cba 2}){( cba

22 )()()(2)( ccbaba 222 222 cbcacbaba

acbcabcba 222222 () zxyzxy

: zxyzxy

2)( zxyzxy 2)}({ zxyzxy

22 )()()(2)( zxyzzxyzxyxy 222222 )())((2)(22 zxzxyzyzyzxzxyyx 222222222 222 xyzzxyyzxxzzyyx



() rqp 523 :

rqp 523 2)523( rqp

2)}52(3{ rqp 22 )52()52()3(2)3( rqrqpp

222 )5()5)(2(2)2(30129 rrqqqrpqp 222 520430129 rqrqqrpqp qrqrpqrqp 203012549 222

() 222 587 cba :

222 587 cba 2222 )587( cba

2222 )}58(7{ cba 22222222 )58()58)(7(2)7( cbcbaa

22222222224 )5()5)(8(2)8(7011249 ccbbcabaa 422422224 2580647011249 ccbbcabaa 222222444 7080112256449 cacbbacba

() 222 zyx

: 222 zyx

2222 )( zyx 2222 }){( zyx

22222222 )()()(2)( zzyxyx 422224224 222 zzxzxyyxx 222222444 222 zxzyyxzyx

:

() 22 )())((2)( yxyxyxyx

() 22 )3()3)(32(2)32( ababbaba () 2222222222 )73()73)(73(2)73( yxyxyxyx () 22 )5()5)(216()8( yxyxyxyx () )352)(235(2)352()235( 222222 xxxxxxxx



() 22 )())((2)( yxyxyxyx :

, ayx byx 22 2 baba 2ba 2yxyx [ a b ] 22x

24x

() 22 )3()3)(32(2)32( ababbaba :

, xba 32 yab 3

22 2 yxyx 2yx 2)}3(32{ abba [ x y ] 2332 abba 23a 29a

() 2222222222 )73()73)(73(2)73( yxyxyxyx :

2222222222 )73()73)(73(2)73( yxyxyxyx 22222 )}73()73{( yxyx 22222 )7373( yxyx 22)6( x 436x



() 22 )5()5)(216()8( yxyxyxyx :

22 )5()5)(216()8( yxyxyxyx 22 )5()5)(8(2)8( yxyxyxyx

, ayx 8 byx 5 22 2 baba 2ba

2)}5()8{( yxyx [ a b ] 258 yxyx 23x 29x

() 2222222 )352)(235(2)352()235( xxxxxxxx :

)352)(235(2)352()235( 222222 xxxxxxxx , axx 235 2

bxx 352 2 abba 222 22 2 baba 2ba

222 )}352()235{( xxxx [ a b ]

222 352235 xxxx 24 16



: () )7)(7( xx () )135)(135( xx () ))(( yzxyyzxy () ))(( baxbax () )4)(3( aa () )4)(3( axax () )136)(176( xx () ))()(( 442222 bababa () ))(( czbyaxczbyax () )53)(103( aa () )325)(325( cbacba () )3)(5( byaxbyax () )7)(7( xx :

)7)(7( xx 22 )7()( x

492 x () ))(( yzxyyzxy :

))(( yzxyyzxy 22 )()( yzxy

2222 zyyx () )4)(3( aa :

)4)(3( aa , abxbaxbxax )(2 )4)(3( aa

)4)(3()43(2 aa 1272 aa

() )135)(135( xx :

)135)(135( xx 22 )13()5( x

16925 2 x () ))(( baxbax :

))(( baxbax 22 )()( bax

222 bxa () )4)(3( axax :

)4)(3( axax , abxbaxbxax )(2

)4)(3( axax )4)(3()43()( 2 axax

12722 axxa



() )136)(176( xx :

)136)(176( xx , abxbaxbxax )(2

)136)(176( xx )13)(17(6)1317()6( 2 xx

221436 2 xx () ))(( czbyaxczbyax :

))(( czbyaxczbyax

)}())}{((){( czbyaxczbyax 22 )()( czbyax })())((2){( 2222 czczbybyxa 222222 2 zcbcyzybxa

() )325)(325( cbacba :

)325)(325( cbacba )}3()25)}{(3()25{( cbacba

22 )3()25( cba 222 )3()2()2)(5(2)5( cbbaa 222 942025 cbaba

() ))()(( 442222 bababa :

))()(( 442222 bababa )}()(){( 442222 baba

))(( 4444 baba 2424 )()( ba

88 ba () )53)(103( aa :

)53)(103( aa , abxbaxbxax )(2 )53)(103( aa

)5)(10(3)510()3( 2 aa 503)15(9 2 aa

50459 2 aa () )3)(5( byaxbyax )}3())}{(5(){( byaxbyax :

)3)(5( byaxbyax , abxbaxbxax )(2 )3)(5())(35()( 2 byaxbyax

15)(8)())((2)( 22 byaxbybyaxax 15)882 2222 byaxybabxyxa



6,4 ba 3c 22222 16164 cbcabba : , 6,4 ba

3c 22222 16164 cbcabba 22 )4(422)2( bcbcabab 2)42( bcab 2)364642( [a, b c ] 2)7248( 2)24( 576

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aa

224 22 [ ] 2)216( 2 2)14( 2 2196 194 7,6 nm , 2222222222 )23(49)23)((56)(16 nmnmnmnm

: , anm 22 bnm 22 23 2222222222 )23(49)23)((56)(16 nmnmnmnm 22 )(49))((56)(16 bbaa 22 )7()7)(4(2)4( bbaa 2)74( ba 22222 )}23(7)(4{ nmnm [ ]



22222 }142144{ nmnm 222 }1025{ nm 222 )})7(10)6(25{ [ m n ] 2}49103625{ 2}490900{ 2}410{ 168100

maa 1 , , 24

1 244

4 mma

a

:

, 41

aa

, 241 24

44 mm

aa

44 1

aa

2

2

22 1

aa

22

2

22 121

aa

aa

2121

22

aa

aa

22 22 m [ ] 2)2( 22 m 2)2(22)( 2222 mm 244 24 mm 24 24 mm =



241 2444 mm

aa ( )

41

xx , , 18

1 22

xx

:

, 41

xx

, 181 22

xx

22 1

xx

xx

xx 121

2

2)4( 2 [ ] 216 18 =

181 22

xx ( )

21

m

m , , 21

44

mm

:

, 21

m

m

, 21

44

mm

44 1

mm



2

2

22 1

mm

22

2

22 121

mm

mm

2121

22

mm

mm

222 22 [ ] 2)24( 2 2)2( 2 24 2 =

2144

mm ( )

12 yx 27xy , 2)( yx 22 yx

: , 12 yx

27xy 2)( yx xyyx 4)( 2 274)12( 2 108144 36 xyyxyx 2)( 222 272)12( 2 54144 90



13 ba 3 ba , 22 22 ba ab : , 13 ba

3 ba 22 22 ba

)(2 22 ba 22 )()( baba )3()13( 2 9169 178

22

22

babaab

22

23

213

49

4169

49169

4160

40

: () )7)(35( qpqp () )87)(96( abba () )57)(53( yxyx () )135)(135( xx



() )7)(35( qpqp :

,

22

22

babaab

22

2735

2735735

qpqpqpqpqpqp

22

2735

2735

qpqpqpqp

22

2104

246

qpqp

22

2)52(2

2)23(2

qpqp

22 )52()23( qpqp

() )87)(96( abba

:

,

22

22

babaab

22

2)87()96(

2)87()96()87)(96(

abbaabbaabba

22

28796

28796

abbaabba

22

2214

2216

baab

22

2)7(2

2)8(2

baab

22 )7()8( baab



() )57)(53( yxyx :

,

22

22

babaab

22

2)57()53(

2)57()53()57)(53(

yxyxyxyxyxyx

22

25753

25753

yxyxyxyx

22

2102

210

yxx

22

2)5(2)5(

yxx

22 )5()5( yxx

() )135)(135( xx

:

,

22

22

babaab

22

2)135()135(

2)135()135()135)(135(

xxxxxx

22

2135135

2135135

xxxx

22

226

210

x

22 )13()5( x



4.2 yx 23 : 32233 2)2()3(32)3(33)23( yyxyxxyx 3223 843329327 yyxyxx 3223 8365427 yxyyxx

ba 52 : 32233 5)5()2(35)2(32)52( bbabaaba 3223 12525235438 bbabaa 3223 125150608 babbaa

nm 2 :

32233 2)2(32)(3)2( nnmnmmnm 3223 84323 nnmnmm 3223 8126 nmnnmm

yx 54 :

32233 5)5(35)4(34)54( yymyxxyx 3223 1252543516364 yyxyxx 3223 12530024064 yxyyxx

: 32233 33 babbaaba

: )(3333 baabbaba

: 32233 33 babbaaba

: )(3333 baabbaba



zyx : 3}{)( zyxzyx 3223 )()(3)(3 zzyxzyxyx 322223223 33)2(333 zyzxzyxyxzyxyyxx 322223223 3336333 zyzxzzyxyzzxyxyyxx

xyzyzxzzyzxxyyxzyx 6333333 222222333

bcab :

3)( bcab 3223 )()(3)(3)( bcbcababab 33222233 33 cbcabbbcbaba 23323333 33 cabcbacbba

yx 52 :

3)52( yx

3223 )5()5(235)2(3)2( yyxyxx 3223 1252564158 yyxxyx 3223 125150608 yxyyxx

: :

bcab yx 52 zyx 32



zyx 32 :

3)32( zyx 3)})32{( zyx

3223 )().32.(3.)32(3)32( zzyxzyxyx 32223223 )32(3})3()3)(2(2)2{(3)3()3.(2.33.)2(3)2( zyxzyyxxzyyxyxx

322223223 962736122754368 zyzzxzyxyzzxyxyyxx xyzyzzxzyxyzxyxzyx 369627541236278 222222333

:

3223 )2()2)(24(3)2()24(3)24( nmnmnmnmnmnm : , anm 24 bnm 2 3223 33 babbaa 3)( ba 3)224( nmnm 3)5( m 3125m

: )93)(84)((3)93()84( 33 bababababa

: , xba 84 yba 93 )93()84( babayx baba 9384 ba xyyxyx )(333 )(333 yxxyyx 3)( yx 3)( ba 3223 33 babbaa



3 ba 2ab , 33 ba : : )(3)( 333 baabbaba 323)3( 3 1827 9

10 yx 30xy , 33 yx : : )(3)( 333 yxxyyxyx 10303)10( 3 9001000 1900 4 yx , xyyx 1233 : : xyyxxyyx 4312 3333 xyyxyx )(333 )(333 yxxyyx )(333 yxxyyx 3)( yx 3)4( 64

71

a

a , 33 1

aa :

:

33

33 11

aa

aa

)1(13)1( 3a

aa

aa

a

)7(3)7( 3 32221343



2m , 3365427 23 mmm :

5)2()2()3(32)3(3)3( 323 mmm 5)23( 3 m 5)223( 3 [ m ]

5)8( 3 5512

507

)65)(67(6)65()67( 33 xxxxx :

, ax 67 bx 65

6567 xxba x2

abbaba )(333 )(333 baabba

3)( ba

3)2( x

38x

: : )65)(67(6)65()67( 33 xxxxx

10 ba 21ab , 33 ba

31

aa , , 18

13

3 a

a



10 ba 21ab , 33 ba : , 10 ba

21ab

, )(3)( 333 baabbaba )10(213)10( 3 6301000 370

370.

31

aa , , 18

13

3 a

a : ,

31

aa

, 3

3

)3(1

aa [ ]

, 2711..31

33

aa

aa

aa

, 27331

33

aa [ 3

1

aa ]

, 9271

33

aa

, 181

33

aa

18133

aa ( )



34 827 xyx :

34 827 xyx )827( 33 yxx })2()3({ 33 yxx

})2()2()3()3){(23( 22 yyxxyxx )469)(23( 22 yxyxyxx

33 8124 yx :

33 8124 yx )278(3 33 yx })3()2({3 33 yx

})3()3()2()2){(32(3 22 yyxxyx )964)(32(3 22 yxyxyx

)2( x 42 24 xx :

)42)(2( 242 xxx })2(2)){(2( 22222 xxx 332 )2()( x

86 x

: ))(( 2233 babababa

: ))(( 2233 babababa



)54( ba 22 252016 baba :

)252016)(54( 22 bababa })5(54)4){(54( 22 bbaaba 33 )5()4( ba

33 12564 ba

ba 32 22 964 baba :

)964)(32( 22 bababa })3()3)(2()2){(32( 22 bbaaba

33 )3()2( ba 33 278 ba

33 278 ba

827 3 a :

827 3 a

33 )2()3( a })2(2.3)3){(23( 22 aaa

)469)(23( 2 aaa

: ba 32 22 964 baba

827 3 a



. : () yx 3 () yx 2 () qp 25 () dcba 22 () 76 p

() byax () 22 32 rp () 23 x () pnm 532

() 222 zyx () 2222 dcba () cbba 32 () 33 2 yx () ba 1211 () 33 yx () yx 3 : 32233 )()3(3)3(33)3( yyxyxxyx 3223 339327 yyxyxx 3223 92727 yxyyxx () yx 2 :

322223232 )()(3)(3)( yyxyxxyx

32246 33 yyxyxx 32246 33 yyxyxx

() qp 25 : 32233 2)2()5(32)5(35)25( qqpqppqp 3223 84532253125 qqpqpp 3223 860150125 qpqqpp

() dcba 22 :

3222222232322 )()(3)(3)( dcdcbadcbabadcba 3624222436 33 dcdcbadcbaba 3624222436 33 dcdbcadcbaba



() 76 p :

32233 7)7()6(37)6(36)76( pppp 34349637363216 23 ppp 343882756216 223 pqqpp

() byax :

32233 )()(3)(3)( bybyaxbyaxaxbyax 33222233 33 ybybaxbyxaxa 33222233 33 ybxyabybxaxa

() 22 32 rp :

3222222232322 3)3()2(33)2(32)32( rrprpprp

642246 279233438 rrprpp

642246 2754368 rrprpp

() 23 x :

323233333 2)2()(32)(3)2( xxxx 84323 369 xxx 8126 369 xxx

() pnm 532 : 3)532( pnm 3)}5()32{( pnm 3223 5)5()32(3)5()32(332 ppnmpnmnm })3()3()2(33)2(32{ 3223 nnmnmm

3222 12525)32(3})3(322)2{(15 ppnmnnmmp



}9124{152796498 223223 nmnmpnnmmnm

32 125)32(75 pnmp pnmnppmnmnnmm 223223 135180602754368

222 125225150 pnpmp mnpppnmpmnpmnmpnm 180225135150546036125278 222222333

() 222 zyx : 3222 )( zyx 3222 )}(){( zyx

3222222222322 ))((3)(3 zzyxzyxyx 32222222223222222232 ))((3)(3})()(3)(3{ zzyxzyxyyxyxx

62242222222642246 )(3})(2){(333 zyxzyyxxzyyxyxx 624242622224642246 3336333 zyzxzzyzyxzxyyxyxx 424226222244224666 3336333 zyzxzyzyxzxyxyxzyx

() 2222 dcba :

322222222222232232222 )()(3)(3)( dcdcbadcbabadcba 664422224466 33 dcdcbadcbaba

() cbba 32 :

3323232232332 )()(3)(3)( cbcbbacbbabacbba 3926232436 33 cbcbbacbbaba

392725436 33 cbcbacbaba



() 33 2 yx :

3323332333333 2)2()(32)(3)2( yyxyxxyx

963369 8126 yyxyxx

() ba 1211 :

32233 12)12()11(312)11(311)1211( bbabaaba 3223 1728475243561331 babaa

() 33 yx :

3323332333333 )()(3)(3)( yyxyxxyx

963369 33 yyxyxx

: () 3223 )3()3)(3(3)3()3(3)3( yxyxyxyxyxyx () 3223 )25()25)(52(3)25()52(3)52( pqpqqppqqpqp () 3223 )2()2)(2(3)2()2(3)2( yxyxyxyxyxyx () 3223 )46()46)(26(3)46()26(3)26( mmmmmm () )(6)()( 2233 yxxyxyx

() 3223 )3()3)(3(3)3()3(3)3( yxyxyxyxyxyx

: , ayx 3 byx 3

3223 33 babbaa 3)( ba

3)33( yxyx 3)6( x 3216x



() 3223 )25()25)(52(3)25()52(3)52( pqpqqppqqpqp : , aqp 52 bpq 25 pqqpba 2552

q10

3223 33 babbaa 3)( ba

3)10( q 31000q ()

3223 )2()2)(2(3)2()2(3)2( yxyxyxyxyxyx : , ayx 2 byx 2 )2()2( yxyxba

yxyx 22 y4

3223 33 babbaa

3)( ba

3)4( y 364 y

() 3223 )46()46)(26(3)46()26(3)26( mmmmmm : , am 26 bm 46 )46()26( mmba

4626 mm 6



3223 33 babbaa

3)( ba

3)6( 216

() )(6)()( 2233 yxxyxyx :

)(6)()( 2233 yxxyxyx ))((23)()( 33 yxyxxyxyx

, ayx byx yxyxba

x2 6

))((23)()( 33 yxyxxyxyx abbaba )(333 )(333 baabba 3)( ba

3)2( x 38x

8 ba 15ab , 33 ba ? :

, 8 ba 15ab

33 ba

)(3)( 3 baabba 8153)8( 3 360512 152



yx 2 , , 8633 xyyx :

, 2 yx , 8633 xyyx

xyyx 633 2.333 xyyx )(333 yxxyyx yx 2 3)( yx 3)2( 8 =

8633 xyyx ( )

yx 1332 6xy , 33 278 yx : , 1332 yx

6xy

33 278 yx

33 )3()2( yx )32(323)32( 3 yxyxyx )13(18)13( 3 xy 13618)13( 3 14042197 793 793.



qp 5 , 3pq , 33 qp :

, 5 qp 3pq

33 qp

)(3)( 3 qppqqp )5(33)5( 3

45125 170

170.

yx 32 , xyyx 188 33 ? : , 32 yx

xyyx 188 33 3)2()(3)2()( 33 yxyx )2)(2(3)2()( 33 yxyxyx yx 23

3)2( yx

3)3(

27 27.

534 x , , 1251802764 3 xx : , 534 x

, 1251802764 3 xx xx 1802764 3

xx 180)3()4( 33

xxxx 180)34(3.4.3)34( 3 xx 180)5.(36)5( 3



xx 180180125 125 = = ( )

3a 2b , 3223 2754368 babbaa : , 3a

2b

3223 2754368 babbaa 3223 )3()3.(2.33.)2.(3)2( bbabaa

3)32( ba

3)}2(3)3(2{

3)66(

3)0( 0

0.

7a , 1126 23 aaa : , 7a

1126 23 aaa 7)2()2.(.32.).(3)( 3223 aaa

7)2( 3 a 7}27{ 3 7)9( 3 7729 722

722.



5x , 6448123 xxx : , 5a

6448123 xxx

3223 )4()4.(.34.).(3)( xxx

3)4( x

3}45{

3)1( 1

1.

222 cba , , 622266 3 ccbaba : , 222 cba ,

622266 3 ccbaba

22266 3 cbaba

2223232 3)()( cbaba

2222222322 3)(.3)( cbabababa

22222232 3)(.3)( cbacbac

6c =

= ( )

41

xx , , 52

13

3 x

x :

, 41

xx

, 521

33

xx



33 1

xx

33 1)(

xx

xx

xx

xx 1131

3

434 3 1264 52 =

= ( )

51

aa , 3

3 1a

a ? :

, 41

aa

33 1

aa

33 1)(

aa

aa

aa

aa 1131

3

535 3 15125 140

140.



: () ))(( 422422 bbaaba () ))(( 2222 ybabxyxabyax () )124)(12( 2422 abbaab () ))(( 2242 aaxxax () )162849)(47( 22 bababa () )18)(124)(12( 32 aaaa () ))()()(( 2222 aaxxaxaaxxax () )27125)(91525)(35( 3322 babababa

() ))(( 422422 bbaaba :

))(( 422422 bbaaba })()){(( 22222222 bbaaba

3232 )()( ba 66 ba

() ))(( 2222 ybabxyxabyax :

))(( 2222 ybabxyxabyax })()){(( 22 byabxyaxbyax 22 )()( byax 2222 ybxa

() )124)(12( 2422 abbaab :

)124)(12( 2422 abbaab })1(1.2)2){(12( 22222 ababab 332 )1()2( ab 18 63 ba



() ))(( 2242 aaxxax :

))(( 2242 aaxxax })(.)){(( 22222 aaxxax 332 )()( ax 36 ax

() )162849)(47( 22 bababa :

)162849)(47( 22 bababa })4(47)7){(47( 22 bbaaba 33 )4()7( ba

33 64343 ba

() )18)(124)(12( 32 aaaa :

)18)(124)(12( 32 aaaa )18}()1(12)2){(12( 322 aaaa )18}()1()2{( 333 aa )18)(18( 33 aa

223 )1()8( a 164 6 a

() ))()()(( 2222 aaxxaxaaxxax :

))()()(( 2222 aaxxaxaaxxax ))(( 3333 axax

2323 )()( ax 66 ax



() )27125)(91525)(35( 3322 babababa :

}27125}{)3(35)5){(35( 3322 babbaaba )27125}()3()5{( 3333 baba )27125)(27125( 3333 baba 2323 )27()125( ba 66 72915625 ba

: () 83 a () 3438 3 x () 34 278 aba () 18 3 x () 33 12564 ba () 633 64729 cba () 3333 6427 cbba () 33 18956 yx () 83 a :

83 a 33 )2()( a })2(2)){(2( 22 aaa

)42)(2( 2 aaa

() 24 278 aba :

34 278 aba )278( 33 baa })3()2{( 33 baa })3(32)2){(32( 22 aaaa

)964)(32( 2 aaaa

() 3438 3 x :

3438 3 x 33 )7()2( x })7(72)2){(7( 22 xxx

)49144)(7( 2 xxx

() 18 3 x :

18 3 x 33 )1()2( x })1(12)2){(12( 22 xxx

)124)(12( 2 axa



() 33 12564 ba :

33 12564 ba 33 )5()4( ba })5(54)4){(54( 22 bbaaba

)252016)(54( 22 bababa () 3333 6427 cbba :

3333 6427 cbba })4()3{( 333 cab })4(43)3){(43( 223 ccaacab

)16129)(43( 223 cacacab

() 633 64729 cba :

633 64729 cba 323 )4()9( bca })4(49)9){(49( 22222 bcbcaacba

)163681)(49( 42222 cbabcabca () 33 18956 yx :

33 18956 yx )278(7 33 yx })3()2{(7 33 yx })3(32)2){(32(7 22 yyxxyx

)964)(32(7 22 yxyxyx



4.3

65 xx : , 5 6 6 ( 1, 6 ) ( 2, 3 )

( 2, 3 ) 3 + 2 = 5 2 3 = 6

63265 22 xxxxx )2(3)2( xxx

)3)(2( xx

54152 xx :

, 15 54 , , ,

54 (1, 54), (2, 27), (3, 18), (6, 9) (6, 9 ) = 6 + 9 = 15 ( 6 ) ( 9) = 54

54965415 22 xxxxx )6(9)6( xxx

)9)(6( xx

1522 xx :

, 2 (15) , , , ,

(15) (1, 15), (3, 5) (3, 5) = 3 + 5 = 2

1535152 22 xxxxx )5(2)5( xxx

)2)(6( xx



2832 xx :

, (3) (28) , , , ,

(28) (1, 28), (2, 14) (4, 14) (3, 5) = 3 + 5 = 2

1535152 22 xxxxx )5(2)5( xxx

)2)(6( xx

72182 xx :

72182 xx 726122 xxx )12(6)12( xxx )6)(12( xx

132232 xx :

132232 xx 13211122 xxx )12(11)12( xxx )11)(12( xx

3692 xx :

3692 xx 363122 xxx )12(3)12( xxx )3)(12( xx

:

72182 xx 3692 xx 132232 xx



1092 2 xx : , 2 10 = 20 [ 2x ] , 4 5 =20 4 + 5 = 9

105421092 22 xxxxx )2(5)2(2 xxx

)52)(2( xx

103 2 xx : , 3 ( 10) = 30 [ 2x ] , ( 5) 6 = 30 5 + 6 = 1

10653103 22 xxxxx )53(2)53( xxxx

)2)(53( xx

33234 2 xx : , 4 33 = 132 [ 2x ] , ( 11) ( 12) = 23 ( 11) + ( 12) = 23

331211433234 22 xxxxx )114(3)114( xxxx

)3)(114( xx

499 2 xx : , 9 ( 4) = 36 [ 2x ] , 3 ( 12) = 9 + 3+( 12) = 9

43129499 22 xxxxx )43(1)43(3 xxxx

)13)(43( xx



9188 2 xx :

9188 2 xx 96128 2 xxx )32(3)32(4 xxx )34)(32( xx 2062 2 aa

: 2062 2 aa 204102 2 aaa )5(4)5(2 aaa )42)(5( aa )2)(5(2 aa

21527 2 xx : 21527 2 xx 26927 2 xxx )13(2)13(9 xxx )29)(13( xx

. 3753 xx 224 yx aay 483 2 222 2 pbaba 9616 22 aay 38 apa 33 162 ba 1222 xyyx 1222 baba 16 24 xx 21236 xx 66 yx 33)( zyx 33 864 yx 40142 xx 12072 xx 650512 xx 22 127 baba 22 802 bpqp 22 403 yxyx 40)(3)( 222 xxxx

: 9188 2 xx 21527 2 xx 2062 2 aa



88)(18)( 22222 baba 180)7(8)7( 222 aaaa )352()43( 222 babaxbax 156 2 xx )2)(1(2 aaxx 4113 2 xx 12163 2 xx 3592 2 xx 22 252 yxyx 33 )(8 yxx 22 61110 qpqp 2)(3)(2 2 yxyx axaax )1( 22 22 121115 yxyx 3223 233 babbaa 3753 xx

: 3753 xx )251(3 2xx })5()1{(3 2xx )51)(51(3 xxx aay 483 2

: aay 483 2 )16(3 2 ya })4(){(3 22 ya )4)(4(3 yya

9616 22 aay : 9616 22 aay )33..2()4( 222 aay 22 )3()4( ay )}3(4)}{3(4{ ayay )34)(34( ayay

224 yx : 224 yx 22 )()2( yx )2)(2( yxyx

222 2 pbaba : 222 2 pbaba 22)( pba ))(( pbapba

38 apa :

38 apa )8( 3pa 33 )()2( pa ).22)(2( 22 pppa )24)(2( 2pppa



33 162 ba : 33 162 ba )8(2 33 ba })2(){(2 33 ba })2(2.)){(2(2 22 bbaaba )42)(2(2 22 bababa

1222 baba

: 1222 baba )1(2)1( 2 aba )1(2)1)(1( abaa )21)(1( baa

21236 xx : , 36 1 = 36 , (6) (6) = 36 6 +(6) = 12 21236 xx 36662 xxx )6(6)6( xxx )6)(6( xx 2)6( x

33)( zyx :

33)( zyx })()}{(){( 22 zzyxyxzyx

)2)(( 222 zyzxzyxyxzyx )2)(( 222 xzyzxyzyxzyx

1222 xyyx : 1222 xyyx 12 22 yxyx 22 )1()( yx )1)(1( yxyx

16 24 xx : 16 24 xx 22222 411..2)( xxx 222 )2()1( xx )21)(21( 22 xxxx )12)(12( 22 xxxx

66 yx :

66 yx 2323 )()( yx

))(( 3333 yxyx ))()()(( 2222 yxyxyxyxyxyx ))()()(( 2222 yxyxyxyxyxyx

33 864 yx :

33 864 yx )8(8 33 yx

})()2{(8 33 yx })(.2)2){(2(8 22 yyxxyx

)24)(2(8 22 yxyxyx



40142 xx : , 40 1 = 40 , 4 10 = 40 4 +10 = 14 40142 xx 401042 xxx )4(10)4( xxx )10)(4( xx

650512 xx : , 1 ( 650 ) = 650 , ( 26) (25) = 650 ( 26) + ( 25) = 51 650512 xx 65025262 xxx )26(25)26( xxx )25)(26( xx

22 802 bpqp : , 1 ( 80) = 80 , 10 8 = 80 10 + ( 8) = 2

22 802 bpqp 22 80810 qpqpqp )10(8)10( qpqqpp )8)(10( qpqp

12072 xx : , 1 ( 120) = 120 , 15 ( 8) = 120 8 +15 = 7 12072 xx 1208152 xxx )15(8)15( xxx )8)(15( xx

22 127 baba : , 1 12 = 12 , 4 3 = 12 3 + 4 = 7 22 127 baba 22 1243 bababa )3(4)3( babbaa )4)(3( baba

22 403 yxyx : , 1 ( 40) = 40 , 5 8 = 40 ( 8) + 5 = 3

22 403 yxyx 22 4058 yxyxyx )8(5)8( yxyyxx )5)(8( yxyx



40)(3)( 222 xxxx : , axx )( 2

= 4032 aa , 1 ( 40) = 40 , 5 8 = 40 8 + ( 5) = 3 , 4032 aa 40582 aaa )8(5)8( aaa )5)(8( aa )5)(8( 22 xxxx

180)7(8)7( 222 aaaa : , xaa )7( 2

= 18082 xx , 1 ( 180) = 180 , 18 10 = 180 18 + 10 = 8 , 18082 xx

18010182 xxx )18(10)18( xxx

)10)(18( xx )107)(187( 22 aaaa

)1025)(1829( 22 aaaaaa )}5(2)5()}9(2)9({ aaaaaa

)2)(5)(2)(9( aaaa )9)(5)(2)(2( aaaa

88)(18)( 22222 baba : , xba )( 22

= 88182 xx , 1 ( 88) = 88 , 4 22 = 88 4 + ( 22) = 18 , 88182 xx 884222 xxx )22(4)22( xxx )4)(22( xx )4)(22( 2222 baba

)352()43( 222 babaxbax :

)352()43( 222 babaxbax )3232()43( 222 bababaxbax

)}32()32({)43(2 babbaaxbax ))(32()43(2 babaxbax

))(32()()32(2 babaxbaxbax )32)(()32( baxbabaxx

))(32( baxbax )32)(( baxbax



156 2 xx : , 6 ( 15) = 90 , 9 10 = 90 9 + ( 10) = 1 , 156 2 xx 151096 2 xxx )3(5)32(3 xxx )53)(32( xx

4113 2 xx : , 3 ( 4) = 12 , 12 1 = 12 12 + ( 1) = 11 , 4113 2 xx 4123 2 xxx )4(1)4(3 xxx )13)(4( xx 12163 2 xx : , 3 ( 12) = 36 , ( 18) 2 = 36 18 + 2 = 16 , 12163 2 xx 122183 2 xxx )6(2)6(3 xxx )23)(6( xx 22 252 yxyx : , 2 2 = 4 , ( 4) ( 1) = 4 4 1 = 5 , 22 252 yxyx 22 242 yxyxyx )2()2(2 yxyyxx )2)(2( yxyx

)2)(1(2 aaxx :

)2)(1(2 aaxx )11)(1(2 aaxx

)1(2 mmxx [ a + 1 = m ] mmxx 22 mxmx 22 mxmx 22

)(1))(( mxmxmx )1)(( mxmx

}1)1(){1( axax )11)(1( axax

)2)(1( axax 3592 2 xx : , 2 ( 35) = 70 , ( 14) 5 = 70 14 + 5 = 9 , 3592 2 xx 355142 2 xxx )7(5)7(2 xxx )52)(7( xx 33 )(8 yxx :

33 )(8 yxx 33 )}(2{)( yxx

33 )22()( yxx })22()22())}{(22({ 22 yxyxxxyxx

})2(2.2.2)2(22){22( 2222 yyxxxyxxyxx )48423)(2( 222 yxyxxyxxy

)4107)(2( 22 yxyxxy



22 61110 qpqp : , 6 10 = 60 , 15 4 = 60 15 +( 4) = 11 , 22 61110 qpqp 22 641510 qpqpqp )32(2)32(5 qpqqpp )25)(32( qpqp

axaax )1( 22 :

axaax )1( 22 axxaax 22

)(1)( axaxax )1)(( axax

22 121115 yxyx : , 15 ( 12) = 180 , ( 20 ) 9 = 180 20 + 9 = 11 , 22 121115 yxyx

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