kn³kmμkarnibnæ nig eroberog μkarrtytbinitübec©kets · 2012. 6. 11. · emeronti9 rbu)ab 096...

i

KN³kmμkarniBnæ nig eroberog

lwm plÁún nig Esn Bisidæ

KN³kmμkarRtYtBinitübec©keTs

elak lwm qun elak Gwug sMNag elak nn; suxNa elakRsI Tuy rINa elak RBwm sunitü elak pl b‘unqay elak Titü em:g

KN³kmμkarRtYtBinitüGkçraviruTæ elak lwm miKÁsir

karIkMuBüÚTr½ kBaØa lI KuNÑaka elak Gwug sMNag

ii

Garmáfa esoePAKNitviTüafñak;TI 8 EdlGñksikSakMBugkan;enAkñúgédenH rYmman 11 emeron . enAkñúgemeronnImYy² eyIgxJúM)aneRCIserIslMhat; mk eFVIdMeNaHRsayKMrUy:agek,aHk,aybMput . eKalbMNgénkareroberogcgRkgKWedIm,ITukCaÉksarCMnYysRmab;Gñk sikSakñúgRKb;mCÄdæan nig müa:geTotedIm,IcUlrYmelIksÞÜyvisy½KNitviTüakñúg RbeTskm<úCaeyIg[kan;EtrIkceRmInqab;rhs½Rsbtamsm½yviTüasaRsþTMenIb. esovePAenHminl¥hYseKhYsÉgenaHeT . kMhusqÁgedayGectnaR)akd CamanTaMgbec©keTs nig GkçraviruTæ . ehtuenHeyIgxJMúCaGñkniBnæ rgcaMCanic©nUv mtiriHKn;EbbsßabnaBIGñksikSaRKb;mCÄdæanedaykþIrIkrayedIm,IEklMGesovenH [kan;EtmansuRkitüPaBRbesIreLIgEfmeTot . CaTIbBa©b; xJMú)aTGñkniBnæsUmeKarBCUnBrGñksikSaTaMgGs;mansuxPaBl¥ manR)aCJaQøasév nig TTYl)aneCaKC½yCanic©kñúgkarsikSa .

)at;dMbg éf¶TI 24 ExFñÚ qñaM2010 GñkniBnæ nig RsayRCav lwm plÁún Tel : 017 768 246 Email: [email protected] Website: www.mathtoday.wordpress.com

mailto:[email protected]

http://www.mathtoday.wordpress.com/

iii

matikarerOg eQμaHemeron TMB½r emeronTI1 cMnYnsniTan 001 emeronTI2 sV½yKuN 011 emeronTI3 TMhMsmamaRt nig PaKry 017 emeronTI4 kenSamBICKNit 024 emeronTI5 kenSamsniTan 040 emeronTI6 smIkardWeRkTImYymanmYyGBaØat 064 emeronTI7 vismIkardWeRkTImYymanmYyGBaØat 077 emeonTI8 bøg;kUGredaen nig Rkab 087 emeronTI9 RbU)ab 096 emeronTI10 kareRbobeFobRtIekaN 102 emeronTI11 ctuekaN 111

emeronTI1 cMnYnsniTan

lMhat; !-kñúgcMeNamcMnYnxageRkam etIcMnYnNaxøHEdles μI 5 ?

1

5,

1

5,

1

5,

1

5,

1

5,

1

5

.

@-sresrcMnYnxageRkamCacMnYnTsPaK ³ k> )01.08()1.02(4)102( x> )0001.08()01.02(4)1004( K> )001,08()102()10008( X> )01,07()1,02(4)106()1007( g> )

1000

1(3)

100

1(9)

10

1(68)10(4)100(5

#-sresrcMnYnxageRkamCaRbPaK ³ k> x> 45.28 837.1 K>

50

191 X> 13.0

g> 734.0 $-sresrcMnYnxageRkamCacMnYnTsPaK ³ k>

100

7 x> 000,10

13 K> 42

3 X> 5.2

73

g> 65217

- 1 -


- 2 -

%-bMeBjkñúg eday b¤ [)anRtwmRtUv ³ k>

7

4 7

3 x> 21 3

54. 5398. K> 0 0 X> 12

7 13

7

g> 12

101

13

72 c>

12

101

13

91

^-teRmobcMnYnsniTan 9

8,

12

11,

6

5,

4

3 tamlMdab;ekIn .

&-teRmobcMnYnsniTan 3

1,

8

3,

4

1,

5

2 tamlMdab;cuH.

*-k> etIcMnYnsniTan 9

4,

7

3,

2

1,

5

2 mYyNaEdlFMCageK ?

x> etIcMnYnsniTan 9

2,

10

3,

5

3,

6

5 mYyNaEdltUcCageK ? (-KNna rYc sRmYl ³ k> )

9

52(

8

1

x> )

9

52()

8

13(

K> )7

52(

25

12

X>

8

5

3

1

2

1

g>

4

1

8

5

3

1

2

1 c> 9

45

12

78

28

5

23


q> 2

9

7

5

12

8

32

8

253

.

!0-KNna k>

16

10.

17

11.

5

4 x> 51

26.

16

17.

13

11

K> 22

26.

16

17

13

11

X>

22

21.

16

17

22

21.

8

11

g> 16

17

4

21

8

11 c>

21

11.

7

3

7

3.

21

11

!!-bgðajfa 9

13

4

13

9

13

4

13

!@-eKman f

e

b

a

d

c

b

a

f

e

d

c

b

a...

bgðajfa f

e

b

a

d

c

b

a

f

e

d

c

b

a...

!#> epÞógpÞat;fa ebI d

c

b

a enaH

f

e

d

c

f

e

b

a .

- 3 -


- 4 -

dMeNaHRsay !-kñúgcMeNamcMnYnxageRkam etIcMnYnNaxøHEdles μI 5 ?

1

5,

1

5,

1

5,

1

5,

1

5,

1

5

.

eKman 51

5,5

1

5,5

1

5,5

1

5,5

1

5

nig 51

5

. dUcenHcMnYnEdlesμI 5 KW ³

1

5,

1

5,

1

5

. @-sresrcMnYnxageRkamCacMnYnTsPaK ³ k> )01.08()1.02(4)102(

28.24

08.02.0420

x> )0001.08()01.02(4)1004(

0208.404

0008.002.04400

K> )001,08()102()10008(

008.8020

008.0208000


X> )01,07()1,02(4)106()1007(

27.764

07.02.0460700

g> )1000

1(3)

100

1(9)

10

1(68)10(4)100(5

693.548

003.009.06.0840500

#-sresrcMnYnxageRkamCaRbPaK ³ k>

20

569

100

284545.28

x> 900

1241837.1

K> 50

69

50

191

50

191

X> 99

1313.0

g> 900

313734.0

$-sresrcMnYnxageRkamCacMnYnTsPaK ³ k> 07.0

100

7

x> 0013.0000,10

13

- 5 -


- 6 -

K> 1875.016

3

2

34

X> 175.040

7

5.2

73

g> 02607.0652

17

%-bMeBjkñúg eday b¤ [)anRtwmRtUv ³ k>

7

4 7

3 x> 21 3

K> 54.0 5398.0

X> 12

7 13

7

g> 12

101

13

72

c> 12

101

13

91

^-teRmobcMnYnsniTan 9

8,

12

11,

6

5,

4

3 tamlMdab;ekIn .

eday 9

8

12

11

6

5

4

3

dUcenH 9

8,

12

11,

6

5,

4

3 .


&-teRmobcMnYnsniTan

3

1,

8

3,

4

1,

5

2 tamlMdab;cuH

eday 5

2

3

1

8

3

4

1

dUcenH 4

1,

8

3,

3

1,

5

2 .

*-k> etIcMnYnsniTan 9

4,

7

3,

2

1,

5

2 mYyNaEdlFMCageK ?

eKman 9

4

7

3

5

2

2

1 dUcenH

9

4 CacMnYnsniTanFMCageK .

x> etIcMnYnsniTan 9

2,

10

3,

5

3,

6

5 mYyNaEdltUcCageK ?

eKman 6

5

5

3

10

3

9

2 dUcenH

9

2 CacMnYnsniTanEdltUcCageK. (-KNna rYc sRmYl ³ k>

72

155

72

1649

9

23

8

1)

9

52(

8

1

x> 56

25

56

152175

7

19

8

25)

9

52()

8

13(

K> 175

391

175

47584

7

19

25

12)

7

52(

25

12

X> 15

4

5

8

6

23

8

5

3

1

2

1

- 7 -


g>

4

1

8

5

3

1

2

1

9

20

3

8

6

5

8

25

6

23

c> 275

6

330

72

10

1

72

3724210

3534

9

49

12

72

7

5

17

9

45

12

78

28

5

23

q> 2546

2205

134

45

19

49

45

359919

49

9

7

5

118

19

8

49

2

9

7

5

12

8

32

8

253

!0-KNna k>

34

11

4.17

2.11

16.17.5

10.11.4

16

10.

17

11.

5

4

x> 24

11

17.3.8.2.13

13.2.17.11

51

26.

16

17.

13

11

K> 22

26.

16

17

22

26.

13

11

22

26.

16

17

13

11

176

45

176

221176

22.8

13.171

- 8 -


X> 22

21.

16

17

22

21.

8

11

352

105

22.16

5.21

22.16

)1722(2122.16

21.1721.22

g> 16

17

4

21

8

11

16

45

16

178422

c>

21

11.

7

3

7

3.

21

11

049

0

49

1111

49

11

49

11

!!-bgðajfa 9

13

4

13

9

13

4

13

eKman 9.4

13.13

9.4

)49(13

9.4

4.139.13

9

13

4

13

ehIy 9.4

13.13

9

13

4

13

dUcenH 9

13

4

13

9

13

4

13 .

- 9 -


!@-bgðajfa f

e

b

a

d

c

b

a

f

e

d

c

b

a...

eKman f

e

b

a

d

c

b

a

f

e

d

c

b

a...

EfmGgÁTaMgBIrnwg f

e

b

a..2 eK)an ³

f

e

b

a

d

c

b

a

f

e

d

c

b

a

f

e

f

e

b

a

d

c

b

a

f

e

f

e

d

c

b

a

f

e

b

a

f

e

b

a

d

c

b

a

f

e

b

a

f

e

d

c

b

a

...

)2

(.2

.

..2....2.

!#> epÞógpÞat;fa ebI d

c

b

a enaH

f

e

d

c

f

e

b

a .

eKman d

c

b

a

eK)an d

c

f

e

f

e

b

a )(

eKTaj f

e

d

c

f

e

b

a .

dUcenH ebI d

c

b

a enaH

f

e

d

c

f

e

b

a .

- 10 -

emeronTI10 kareRbobeFobRtIekaN

lMhat; !> DEFABC

cmxEF

cmxBC

)905(

)302(

FE

D KNna BC @> kñúgrUbxageRkam enHeK[

C B

A

nig PRPQ PTSPST eRbobeFob PQS nig PRT P

R Q S T

- 102 -


- 103 -

#> eK[ MBMT nig MOMA bgðajfa MBAMTO $> eK[ nig BCAB CDAD eRbobeFob nig AED CED

M

A O

B

T

A

B

C

DE


- 104 -

%> eK[ nig CDAB // TSTR bgðajfa DCTABT ^> eK[ nig CADBAD BCAD bgðajfa nig ACDABD ACAB

A

B

C

D

T

S

R

A

B D C


dMeNaHRsay !> DEFABC

cmxEF

cmxBC

)905(

)302(

KNna BC D

E F

A

eday DEFABC enaHeK)an EFBC

CB

naM[ 2 90530 xx

60

1202

309052

x

x

xx

cMeBaH 60x eK)an cmBC 15030)60(2 dUcenH . cmBC 150

- 105 -


@> kñúgrUbxageRkam enHeK[ nig PRPQ PTSPST eRbobeFob PQS nig PRT P

eKman PQ naM[ PR PQR sm)at vi)ak . PRQPQR

mü:ageTot enaH PTSPST PST sm)at vi)ak . PTPS

eKman PTRPTSPSTPSQ oo 180180

eday enaHeKTaj PRQPQR RPTQPS dUcenH PQS PRT ¬ tamkrNI C>m>C ¦

Q RS T

- 106 -


- 107 -

#> eK[ MBMT nig MOMA bgðajfa MBAMTO

eKman MBMT nig MOMA ¬ smμtikmμ ¦ ehIy ¬ mMurYm ¦ AMBOMT

dUcenH MBAMTO ¬ tamkrNI C>m>C ¦

M

A O

B

T


- 108 -

$> eK[ nig BCAB CDAD eRbobeFob nig AED CED eKman BCAB nig CDAD enaH ABC nig ADC CaRtIekaNsm)at man ][AC Ca)atrYm . eKTaj)an CabnÞat;BuHénmMu )(BD ABC nig ADC . eday ][BDE enaHeKTaj ECEA . RtIekaN nig AED CED manRCugbIb:unerogKñaCaRtIekaN b:unKña .

A

B

C

DE


- 109 -

%> eK[ nig CDAB // TSTR bgðajfa DCTABT eKman enaH CDAB // TDSRAT ¬ mMuqøas;kñúg ¦ ¬smμtikmμ ¦ TSTR

ehIy DTSATR ¬mMuTl;kMBUl ¦ dUcenH TDSTAR

vi)ak SDAR nig TDTA eKman enaH CDAB // TCSTBR ¬ mMuqøas;kñúg ¦ ¬smμtikmμ ¦ TSTR

ehIy ¬mMuTl;kMBUl ¦ CTSBTR

A

B

C

D

T

S

R


dUcenH TCSTBR

vi)ak SCBR nig TCTB eday SDAR nig SCBR enaH CDAB . dUcenH DCTABT ¬tamkrNI C>C>C ¦ ^> eK[ nig CADBAD BCAD bgðajfa nig ACDABD ACAB

- 110 -

A

B CD

eKman naM[ BCAD ADB nig ADC CaRtIekaNEkg eday ¬tamsmμtikmμ ¦ CADBAD

eKTaj ACBCADBADABC oo 9090 naM[ ABC sm)at . vi)ak ACAB dUcenH . ACDABD

emeronTI11 ctuekaN

- 111 -

lMhat; !-RtIekaN mYyman ABC E nig D CacMnuckNþalén ][AB

nig ][AC erogKñanig 46,49 xBCxDE . KNnatémøén x . @-eKmanctuekaNEkg nigRbelLÚRkam . ABCE BCDE

bgðajfaRtIekaN ACD CaRtIekaNsm)at .

A

B

C

E

D

A

B

C D

EF

emeronTI11 ctuekaN

#-eKmanctuekaNBñay Edl nig ABCD ]//[][ CDAB X nig Y CacMnuckNþalénRCugeRTt . k> KNna AB ebI 6.12XY nig 3DC x> KNnatémø x ebI eKdwgfa 12,112,74 xABxXYxDC . $-eKmanctuekaNBñaysm)at Edl ABCD ]//[][ ADBC nig . KNnargVas;mMuepSgeTot ? oA 67

A B

CD

YX

A

CB

o67

D

- 112 -

emeronTI11 ctuekaN

%-eKman CaRbelLÚRkamEdl ABCD CEAD nig CEDCDE bgðajfa CactuekaNesμI . ABCD

^-eKman CactuekaNesμI . ABCD

eKman ][][],[][ BCDFADEB . bgðajfa DFBE

CB

DA E

A B

C

E

F

D

- 113 -

emeronTI11 ctuekaN

&-eKman CactuekaNesμI . ABCD

bgðajfa nig ODC OCD CamMubMeBjKña ?

A

B

D

O

C

- 114 -

emeronTI11 ctuekaN

- 115 -

dMeNaHRsay !-RtIekaN mYyman ABC E nig D CacMnuckNþalén ][AB

nig ][AC erogKñanig 46,49 xBCxDE . KNnatémøén x .

eKman E nig D CacMnuckNþalén nig [][AB ]AC enaH ED Ca)atmFüménRtIekaN . ABC

eK)an 2

BCED eday 46,49 xBCxDE

eK)an 2

4649x

x

2349 xx naM[ 1x . dUcenH 1x .

A

B

C

E

D

emeronTI11 ctuekaN

- 116 -

@-eKmanctuekaNEkg nigRbelLÚRkam . ABCE BCDE

bgðajfaRtIekaN ACD CaRtIekaNsm)at .

eKman EDAEBC RCug ctuekaNEkg ABCE

nigRbelLÚRkam BCDE naM[ E CacMNuckNþalén AD ehIy eRBaHoCEA 90 ABCE CactuekaNEkg eKTaj)an CaemdüaT½rén CE AD . dUcenH CAD CaRtIekaNsm)at . smÁal; ³ eKman BEAC Ggát;RTUgctuekaNEkg . ABCE

ehIy CDBE RCugRbelLÚRkam BCDE

eKTaj)an CDAC dUcenH CAD CaRtIekaNsm)at .

A

B

C

D

EF

emeronTI11 ctuekaN

- 117 -

#-eKmanctuekaNBñay Edl nig ABCD ]//[][ CDAB X nig Y CacMnuckNþalénRCugeRTt . k> KNna AB ebI 6.12XY nig 3DC x> KNnatémø x ebI eKdwgfa 12,112,74 xABxXYxDC . k> KNna AB ebI 6.12XY nig 3DC eKman X nig Y CacMnuckNþalénRCugeRTt AD nig BC enaH XY Ca)atmFüménctuekaNBañy . eK)an

2

CDABXY

naM[ CDXYAB .2

2.2232.253)6.12(2 AB . x> KNnatémø x ebI eKdwgfa 12,112,74 xABxXYxDC

A B

C D

X Y

emeronTI11 ctuekaN

eK)ansmIkar 2

7412112

xxx

14

11332

33112

x

xx

xx

dUcenH 14x . $-eKmanctuekaNBñaysm)at Edl ABCD ]//[][ ADBC nig . KNnargVas;mMuepSgeTot ? oA 67

eday ABCD CactuekaNBañysm)atenaH oAD 67

ehIy oooo

CB 1132

6767360

dUcenH oAD 67 nig oCB 113

A

C B

o67

D

- 118 -

emeronTI11 ctuekaN

%-eKman CaRbelLÚRkamEdl ABCD CEAD nig CEDCDE bgðajfa CactuekaNesμI . ABCD

eKman A CaRbelLÚRkam enaH BCD BCAD nig CDAB eday enaH CEDCDE CDE CaRtIekaNsm)at vi)ak CECD . tamsmμtikmμ enaHeKTaj CEAD CDAD dUcenH ABCD CactuekaNesμI .

A D E

B C

- 119 -

emeronTI11 ctuekaN

^-eKman CactuekaNesμI . ABCD

eKman ][][],[][ BCDFADBE . bgðajfa DFBE eKman ][][],[][ BCDFADBE enaH ABE nig CDF CaRtIekaNEkg . eKman FCDEAB nig DCAB enaH . CDFABE

vi)ak DFBE .

A B

C

E

F

D

- 120 -

emeronTI11 ctuekaN

&-eKman CactuekaNesμI . ABCD

bgðajfa nig ODC OCD CamMubMeBjKña

A

- 121 -

eKman

2

ADCODC

nig

2

BCDOCD

eK)an ooBCDADC

OCDODC 902

180

2

dUcenH nig CamMubMeBjKña . ODC OCD

B

D

O

C

emeronTI2 sV½yKuN

- 11 -

lMhat; !-cUrsresrplKuNxageRkamCasV½yKuNrYcR)ab;eKal nig niTsSnþ k> 6666666 x> 888888 K>

n

aaaaa ....

X>

n

c

ab

c

ab

c

ab

....

@-cUrsresrsV½yKuNxageRkamCaplKuNktþadUcKñarYcKNna k> 23 24 x> 32 78 K> 34 63 ` X> 33 127 #-cUrsresrsV½yKuNxageRkamCaplKuNktþadUcKñarYcKNna

k> 23 34 x> )2(3

242

23

K> 223 532 X> 343 325 $-ctuekaNEkgmYymanbeNþayRbEvg 13 b nigTTwgRbEvg 12 b KNnabrimaRtctuekaNEkgenaHebI 3b .

emeronTI2 sV½yKuN

- 12 -

%-KNnatémøénkenSamxageRkam ³ k> cMeBaH 22 23 xyyx 5x nig 4y x> cMeBaH ))(65( 3322 nmnm 1m nig 2n

K> cMeBaH 2432 cba 3,2 ba nig 1c ^-sRmYlkenSamxageRkam ³ k> x> )4)(4)(4( 425 743 2222

K> 364

3

4

3

4

3

4

X> 612

23222

743

&-sRmYlkenSamxageRkam ³

k> ))(3( 5734 yxyx x>

42

4332

6

22

3

ba

baba

K> )4)(2)(5(

)5)(32(322

3482

xaxaax

xaxa

X> 33222

382

)4()2)(5(

)32(

xaxaax

xa

g> 42

530

32

6

)2(2

3

ba

baba

emeronTI2 sV½yKuN

- 13 -

dMeNaHRsay !-sresrplKuNxageRkamCasV½yKuNrYcR)ab;eKal nig niTsSnþ k> 766666666 maneKal 6 nig niTnSnþ 7

x> 66 8)8(888888 maneKal 8 nig niTnSnþ . 6

K> n

n

aaaaaa ....

maneKal a nig niTnSnþ n

X> n

n

c

ab

c

ab

c

ab

c

ab

....

maneKal c

ab nig niTnSnþ . n

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cUrrktémøén ebI cba mab 34 .

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- 19 -

dMeNaHRsay !-rktémø x kñúgkrNInImYy²xageRkam ³ k> 5:7:4 x eK)an

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x> d

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g> d

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- 23 -

emeronTI4 kenSamBICKNit

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lMhat; !-KNna k> 222 573 xxx x> tyxtyxtyx 244444 2

2

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én x . x> sresrpldk AB

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K> 5)3(9)3( 22 baba

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c> )5)((6 baba

- 25 -


(-dak;kenSamxageRkamCaplKuNktþa ³ k> 2)12(16)12(9 xx

x> )4(5)123( 2 aaa

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c> byaybxax 88

q> bybxayax 22

- 26 -


!!> dak;kenSamxageRkamCaplKuNktþa k> x> 14252 a 2 b K> 49 2 x X> 22 4 yx

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- 27 -


!$> eK[BhuFa 1582 bbA k> etIeKRtUvykcMnYnNamkbEnßmelI bb 82 edIm,I[)anCakaer éneTVFa ? x> edayeRbIlTæplmundak; A CakaeréneTVFadWeRkTI ! . K> sMNYrdEdlcMeBaHBhuFa 342 xxB nig 384 2 xxC .

- 28 -


dMeNaHRsay !-KNna k> 222222 5510573 xxxxxx x> tyxtyxtyxtyxtyx 2444244444

2

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- 29 -


- 30 -

#-KNnaplbUkxageRkam ³ k> 222222 523 yxyxyx

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ayaaayaxyayxy

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2322


- 31 -

x> 3( ))(2(2)3)(1()2)(1 tttttt

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eKman 32)1(35)1)(1(35 2222 bbbbbb 32)1)(1(35 22 bbbb


- 32 -

&-muFaKNnaedayeRbIsmPaBsMxan;²

eK)an ³

2 10102 222

2222

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k> 9 )169(16)12( 222 xxxx

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222

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xxxx


- 33 -

tag

A )169(16)12(9 222 xxxx

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baba

bababa


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2

44

22

a

a

aa

a

Z> 12

56

127

342

2

2

2

pp

pp

pp

pp

N> 65

107

168

432

2

2

2

nn

nn

nn

nn

- 44 -


t> 168

4

4

2

6

3222

xx

x

x

x

xx

x

f> 31530

2542

351730

723202

2

2

2

xx

xx

xx

xx

T> 3512

25

16

2092

2

2

2

aa

a

a

aa

F> 213712

15224

81449

65562

2

2

2

yy

yy

yy

yy

(> sRmYlkenSamsniTanxageRkam ³

k> 5

1

5

13

1

6

1

x>

4

7

2

53

8

3

2

56

K> 7

5

6

57

5

6

5

X>

xx

x

3

11

3

g> x

x

x

15

3

5

23

2

c>

1

21

3

kk

k

kk

q>

)1(2

x

y

x

y

y

x

x

y

y

x

- 45 -


- 46 -

C>

22

24

ba

ab

ab

b

ba

ab

ba

aba

Q>

abbaba

ba

baba

bba 1112)(2233

22

j>

ba

a

a

ba

ba

b

ba

babaa

baba

aba2

)2(33

22

22

2

d> ab

baaab

baa

1

)(1

1 z> b

b

b

b

2

11

21

2

11

21

!0-k> zyx ,, CacMnYnsniTanxusBIsUnü . ebI

x

y

y

xC

z

x

x

zB

y

z

z

yA ,, cUrbgðajfa ³

CBACBA ..222 minGaRs½ynwg zyx ,, . x> CacMnYnsniTanxusBIsUnü . cba ,,

bgðaj[eXIjfaebI 1abc enaHeK)an ³ )

1)(

1)(

1(4)

1()

1()

1( 222

cc

bb

aa

cc

bb

aa

!!-rktémø x edIm,I[kenSamsniTan )25)(3(2

)62)(15.03(

xx

xx

es μInwgsUnü .


- 47 -

dMeNaHRsay !-KNnatémøelxénkenSamsniTanxageRkam ³ k>

3

)1(3

x

xx cMeBaH 2

1,1 xx nig

3

2x

-cMeBaH 1x enaH 4

1

31

)11(31

3

)1(3

x

xx

-cMeBaH 2

x1 enaH

5

8

32

1

)12

1(3

2

1

3

)1(3

x

xx

-cMeBaH 3

x2 enaH

11

5

33

2

)13

2(3

3

2

3

)1(3

x

xx

x> 12

42

2

aa

a cMeBaH 2

1,2 aa nig 1a

K> 45

32

yy

y cMeBaH 1,0 yy nig 2

1y

-cMeBaH 0y enaH 4

3

4)0(50

30

45

322

yy

y

-cMeBaH 1y enaH 5

1

4)1(51

31

45

322

yy

y


- 48 -

-cMeBaH 2

y1 enaH 2

42

5

4

1

32

1

45

32

yy

y

X> xyx

yx

2

43 cMeBaH 1x nig 4

1y

eK)an 13

8

4

19

13432

xyx

yx

@-rktémøénGefr x edIm,I[kenSamsniTanxageRkammann½y ³ k>

76

7

x

x mann½yluHRtaEt 6 07 x b¤ 6

7x

x> 2)3(

3

x

x mann½yluHRtaEt 03 x b¤ 3x

K> )3)(4(

1

xx

x

mann½yluHRtaEt 0)3)(4( xx b¤ 3,4 xx

X> 16

32122

2

x

xx

mann½yluHRtaEt 0)4)(4(162 xxx

b¤ 4,4 xx .


- 49 -

#-rktémøénGefr edIm,I[kenSamsniTanxageRkamKμann½y a

k> 1a

a Kμann½yluHRtaEt 01 a b¤ 1a . x>

13 a

ab

Kμann½yluHRtaEt 013 a b¤ 1a

K> 1)1(

42

2

a

aa

Kμann½yluHRtaEt 0)2(1)1( 2 aaa

b¤ 2,0 aa

X> aa

a

3

2 9)3(

Kμann½yluHRtaEt 0)1)(1(3 aaaaa

b¤ 1,1,0 aaa $-rktémøénGefr x edIm,I[kenSamsniTanxageRkames μInwgsUnü ³ k>

x

x

2

32

es μIsUnüluHRtaEt 032 x b¤ 2

3x .


- 50 -

x> 1

3 2

x

x es μIsUnüluHRtaEt 0)3)(3(3 2 xxx b¤ 3,3 xx . K>

4

5)12)(5(2

x

xxx

es μIsUnüluHRtaEt 0)22)(5(5)12)(5( xxxxx b¤ 1,5 xx .

X> 12

4)3(2

22

x

xx

es μIsUnüluHRtaEt 0)3)(33(4)3( 22 xxxx

b¤ 3,1 xx . %-sRmYlkenSamsniTanxageRkam ³

k> y

x

yx

x 2

7

142

3

Edl 0,0 yx

x> 2333

42

3

42

8

8

)2(

8

ax

b

xba

xba

abx

xba

Edl 0,, xba


- 51 -

K> ba

x

ba

bax

3

2

)(

)( Edl a b

X> )3(2

1

)3)(3(18

)3(9

)9(18

)3(9222

xaxxba

xab

xba

xab

Edl 3,0,0 xba .

g> y

yx

xy

yxxy

xy

xyyx 2

2

2

2

32 )(

Edl 0,0 yx

c> )51()51(

)51)(51(

15

251 2

xx

xx

x

x

Edl 5

1x

q> 9

)1)(5()3)(1(2

x

xxxx

)3)(3(

)1(8

)3)(3(

)53)(1(

xx

x

xx

xxx

C> )32)(1(7)1(8

)3)(1(2)33(23

2

xxx

xxx

1322

37

)1322)(1(

)37)(1(

)21714888)(1(

)6299)(1(

)32)(1)(1(7)1)(1(8

)3)(1(2)1(9

22

22

2

2

xx

x

xxx

xx

xxxxx

xxx

xxxxxx

xxx


Q> )1()2)(1()17)(1(

)3)(22()32)(1(2

xxxxx

xxxx

1,277

9

)12187)(1(

)2632)(1(

)1()2)(1()17)(1)(1(

)3)(1(2)32)(1(

2

2

xxx

xxxx

xxx

xxxxxx

xxxx

j> mnanama

mnanama

2

2

na

na

na

nama

nama

manmaa

manmaa

,

))((

))((

)()(

)()(

d> bcacaba

bcacaba

2

2

ba

ba

caba

caba

bacbaa

bacbaa

))((

))((

)()(

)()(

Edl . ca

- 52 -


- 53 -

z> yx

yxayax

33

yx

a

yx

ayx

yx

yxyxa

,3

1

)(3

)1)((

)(3

)()(

D> 22

2

aa

aa

2)2)(1(

)1(

a

a

aa

aa Edl 1a

Z> 82

1242

2

aa

aa

2,

4

6

)2)(4(

)2)(6(

)31)(31(

)42)(42(

9)1(

16)2(2

2

aa

a

aa

aa

aa

aa

a

a

N> 22

22

32 baba

ab

ba

ab

baba

abab

32)32)((

))((

Edl b¤ 0 ba ba .


- 54 -

t> 5105

4842

2

xx

xx

5

4

)1(5

)1(42

2

x

x Edl 1x

f> )4)(2(

53

274

53 22

22

22

yxyx

yxyx

yxyx

yxyx

T> 76

211722

2

yy

yy

1

32

)7)(1(

)7)(32(

y

y

yy

yy Edl 7y

^-rkplKuN nig plEckénkenSamsnITanxageRkam ³

k> yx

yx

xy

yx

5

4

10

6

3

44

22

4

3

x> yxyx

xy

xy

yx 2322

2

515

4

54

72

K> b

dac

ab

dc

dc

ba

63

2

4

42

2

54

2

2

X> a

b

b

ba

ba

ba

7

36

90

40

28

64 22

2

33

g> )3(4

)3)(3(

3

)4(

bbb

bb

b

bb


- 55 -

c> )12)(52(

)32)(32(

)53)(53(

)32)(43(

xx

xx

xx

xx

)12)(52)(53)(53(

)32()32)(43( 2

xxxx

xxx

q> yy

y

y

yy

3

9

)3(

32

2

2

2

1)3()3(

)3)(3)(3(2

yyy

yyyy Edl 3,0 yy

C> 2222 2 yxyx

yx

yx

yx

1)(

))((

)( 2

yx

yx

yxyx

yx Edl yx

Q> 2

22

)7(

49

)7(

49

a

a

a

a

7,)7(

)7)(7(

)7)(7)(7)(7(2

aa

aa

aaaa

j> yvxvyuxu

yvxvyuxu

yvxvyuxu

yvxvyuxu

2

2

)(

)(

))()()((

))()()((

yx

yx

vuyxvuyx

vuyxvuyx


d> 34

82

23

12

2

2

2

bb

bb

bb

b

3

4

)3)(1)(2)(1(

)4)(2)(1)(1(

b

b

bbbb

bbbb

Edl . 2,1 bb

z> 824

65

86

623 2

2

xyxy

yy

xx

yxxy

1)3)(2(

)2)(4(

)4)(x2(x

)3)(y2(x

yy

yx

Edl 3,2,4,2 yyxx .

D> 2

2

2

2

1

532

32

152

m

mm

mm

mm

3,1;

)1(

)52(

)1)(1)(3)(1(

)52)(1)(52)(3(

2

2

mmm

m

mmmm

mmmm

Z> nm

nm

nmnm

nmnm

2

2

232

23222

22

nm

nm

nmnmnm

nmnmnm

2

2

)2)(2)(2(

)2)(2)(2(

Edl . nm 2

- 56 -


&> rkplbUk b¤ pldkkenSamsniTanxageRkam ³ k> a

aaaaa2

7

14

7

212

7

2

7

12

x> 714

2

14

3

14

3

14

yyyyyy

K> 1

1

1

1

1

x

x

xx

x

X> 6

3

6

2

6

b

y

b

y

b

y

g> 66666

yx

yx

yx

y

yx

x

c> 3

)(2

3333

x

ba

x

ba

x

ba

x

ba

x

ba

q> baba

baba

ba

ba

ba

b

ba

a

))((2222

C> 2

1

222222

ba

ba

ba

b

ba

a *> rkplbUk b¤ pldkkenSamsniTanxageRkam ³ k>

4

38

4

226

4

2

2

3 yxyxyxyxyx

x> 6

73

6

524

6

5

3

2 yxyxyxyxyx

K> xyz

xz

yzxy

6565

- 57 -


X> abc

ac

bc

a

ab

c

4

3

42

3 22

g> 3

32

3

3

3

2

3

3

62

4

a

a

aa

a

aa

a

c> 22

22

22 )()(

])())[((

)()( baba

bababa

ba

ba

ba

ba

)()(

42 baba

ab

q> ab

ba

ca

ac

bc

cb

00

abcabc

bcacabbcacab

C> dc

b

bc

c

36

2

510

4

)2)(2(15

)510612(2

)2)(2(15

)2(10)2(12

)2(3

2

)2(5

4

22

dcbc

bbccdc

dcbc

bcbdcc

dc

b

bc

c

Q> )4(6

75

)4(6

4233

312

2

82

1

a

a

a

aa

a

a

a

a

- 58 -


j> ))(())(())(( bcac

c

abcb

b

cbba

a

))(())()((

)())((

))()((

)()()(

cbba

a

accbba

bacbaac

accbba

bacacbaca

d> 222 1

1

5

5

4

4

a

a

aa

a

aa

a

)1)(5)(4(

20108

)1)(5)(4(

202025520164

)1)(5)(4(

)5)(4()4)(1(5)5)(1(41

1

5

5

4

4

)1)(1(

1

)5(

5

)4(

4

2

222

aaa

aa

aaa

aaaaaa

aaa

aaaaaaaaa

aa

a

aa

a

aa

a

z> )(

))((

)(

))((

abb

bybx

baa

byax

ab

xy

)(

))(())(()(

baab

bybxabyaxbbaxy

- 59 -


a

x

baab

bxxyxyba

baab

babyxbaxy

baab

abaxabbxbybaxy

)(

))((

)(

))(()(

)(

))(()(

D> 2

2

44

22

a

a

aa

a

)2()2(

1287

)2()2(

)2()2(

2

2

)2(

2

2

23

2

32

2

aa

aaa

aa

aa

a

a

a

a

Z> 12

56

127

342

2

2

2

pp

pp

pp

pp

)4)(1(

212

1

5

4

1

)1(

)5)(1(

)4)(3(

)3)(1(

2

2

pp

pp

p

p

p

p

p

pp

pp

pp

- 60 -


N> 65

107

168

432

2

2

2

nn

nn

nn

nn

)3)(4(

1752

)3)(4(

2034

3

5

4

1

)3)(2(

)5)(2(

)4(

)4)(1(

2

22

2

nn

nn

nn

nnnn

n

n

n

n

nn

nn

n

nn

t> 168

4

4

2

6

3222

xx

x

x

x

xx

x

)4)(2)(2(

124

)4)(2)(2(

4164

4

1

)2)(2(

4

4

1

2

1

2

1

)4(

4

)2)(2(

2

)2)(3(

3

22

2

xxx

xx

xxx

xx

xxxxxx

x

x

xx

x

xx

x

T> 3512

25

16

2092

2

2

2

aa

a

a

aa

)7)(5(

)5)(5(

)4)(4(

)5)(4(

aa

aa

aa

aa

)7)(4(

)5(3

7

5

4

5

aa

a

a

a

a

a

- 61 -


(> sRmYlkenSamsniTanxageRkam ³

k> 4

5

5

116

21

5

1

5

13

1

6

1

x> 10

31

4

710128

32048

4

7

2

53

8

3

2

56

K> 13

1

42

303542

3035

7

5

6

57

5

6

5

X> 0,2

313

3

3

11

3

x

x

x

xx

x

g> )3(5

2

3

)9(53

)3(2

15

3

5

23

2

2

x

x

x

x

x

x

x

x

c> 2

3

2

32

1

21

3

2

2

k

k

kk

kk

kk

k

kk

- 62 -


!!-rktémø x edIm,I[kenSamsniTan

)25)(3(2

)62)(15.03(

xx

xx

es μInwgsUnüluHRtaEt 0)62)(15.03( xx eKTaj 3,05.0 xx .

- 63 -

emeronTI6 smIkardWeRkTI1manmYyGBaØat

lMhat; !-edaHRsaysmIkar k> 1232 x x> 67185 x K> 78299 x X> 35125 a g> 1132 x c> 120168 b q> yy 3258 C> mm 4725 Q> 3253 xx j> 2552 n d> z> aa 640 1723 x @-edaHRsaysmIkar k> 12)3(3 x x> xx 5)4(3 K> )3(5)3(5 xx X> aa 24)6(4 g> nn 18)8(9 c> )4(2)32(7 tt q> )1(3)2(4 xx C> )3(2103 zz Q> )13()3(2 xxx #-edaHRsaysmIkar k> 144

5

3x x> 8

3

1

2

3b

- 64 -


K> 3

2

2

12 x X> 9

2

3

a

g> 154

3

m c> 4

39

4

xx

$-edaHRsaysmIkar k> 0)3( xx x> 0)8(3 xx K> 0)27(12 x X> 0)82)(3( xx g> 0)1)(3( xx c> 0)7)(12( xx q> 092 x C> xx 16642 Q> mm 212 j> 04)3( 2 x

d> 08124 23 aaa z> )1(9)1(4 2 xxx

D> )1)(32()32( 2 xxx

Z> )35(7)35)(3( xxxx N> 22 )65()7( xx

5-enAeBlEdlelakRKUdak;lMhat;[sisSeFIV vibul)aneFIVlMhat;dUcteTA eK[smIkar 2510156 mm dak;GgÁTaMgBIrCaplKuNktþa )52(5)52(3 mm

- 65 -


EckGgÁTaMgBIrnwg )52( m eK)an 52

)52(5

52

)52(3

m

m

m

m

53 etIvibulmankMhusRtg;NakñúgkaredaHRsaysmIkar cUrrkkMhusenaH ? ^-plbUkR)aMcMnYnKt;bnþKñaes μInwg 520 . cUrrkR)aMcMnYnKt;enaH ? &-GayumIgsMesμInwg bIdgénGayusIuNaEdlCakUnrbs;Kat; . kalNasIuNamanGayues μInwgGayurbs;mþaynagsBVéf¶enH plbUkén GayuGñkTaMgBIresμInwg 112 qñaM .rkGayurbs;mIgsM ? *-sUpatmanGayu 51 qñaM egIyrsμImanGayu qñaM . 21

etIryHeBlb:un μanqñaMeTAmuxeToteTIbsUpatmanGayuesμInwg 2 dgén GayursμI ?

- 66 -


- 67 -

dMeNaHRsay !-edaHRsaysmIkar k> 1232 x

2

9

92

3122

x

x

x

x> 67185 x

5

49

495

18675

x

x

x

K> 78299 x

9

49

499

29789

x

x

x

X> 35125 a b¤ 475 a

5

47a


g> 1132 x

7

142

3112

x

x

x

c> 120168 b

13

1048

161208

b

b

b

q> yy 3258

5

255

2538

y

y

yy

C> mm 4725

1

99

2745

m

m

mm

Q> 3253 xx

8

5323

x

xx

- 68 -


j> 2552 n

10

202

5252

n

n

n

d> aa 640

8

405

406

a

a

aa

z> 1723 x

5

153

2173

x

x

x

@-edaHRsaysmIkar k> 12)3(3 x

7

43

x

x

x> xx 5)4(3

6

1253

5123

x

xx

xx

- 69 -


K> )3(5)3(5 xx

3

62

33

x

x

xx

X> aa 24)6(4

5

6

66

66

a

aa

aa

g> nn 18)8(9

3

8

83

28

n

n

nn

c> )4(2)32(7 tt

12

29

2912

822114

t

t

tt

- 70 -


- 71 -

q> )1(3)2(4 xx

11

3384

x

xx

C> )3(2103 zz

4

62103

z

zz

#-edaHRsaysmIkar k> 144

5

3x

30

903

70203

x

x

x

x> 83

1

2

3b

9

44

449

4629

b

b

b

K> 3

2

2

12 x

12 43 x b¤ 12

1x


X> 92

3

a

63

18

a

a

g> 154

3

m

203

60

m

m

c> 4

39

4

xx

9

364

336

x

x

xx

$-edaHRsaysmIkar k> 0)3( xx eK)an 3,0 xx x> 0)8(3 xx eK)an 8,0 xx K> 0)27(12 x naM[ 27x

- 72 -


X> 0)82)(3( xx ebI 03 x enaH 3x ebI 082 x enaH 4x g> 0)1)(3( xx eK)an 1,3 xx c> 0)7)(12( xx eK)an 7,12 xx q> 092 x b¤ 0)3)(3( xx eK)an 3,3 xx C> xx 16642 eK)an b¤ 0)8(6416 22 xxx 8x Q> mm 212 eK)an b¤ 0)1(12 22 mmm 1m j> 04)3( 2 x

eK)an 0)1)(5( xx naM[ 1,5 xx

- 73 -


d> 08124 23 aaa 0)2)(1(4 aaa

eKTaj 2,1,0 aaa z> )1(9)1(4 2 xxx

0)32)(32)(1(

0)94)(1( 2

xxx

xx

eK)an 2

3,

2

3,1 xxx

D> )1)(32()32( 2 xxx

0)4)(32(

0)132)(32(

0)1)(32()32( 2

xx

xxx

xxx

eK)an 4,2

3 xx

N> 22 )65()7( xx

0)14)(136(

0)657)(657(

0)65()7( 22

xx

xxxx

xx

eK)an 4

1,

6

13 xx

- 74 -


5-enAeBlEdlelakRKUdak;lMhat;[sisSeFIV vibul)aneFIVlMhat;dUcteTA eK[smIkar 2510156 mm dak;GgÁTaMgBIrCaplKuNktþa )52(5)52(3 mm EckGgÁTaMgBIrnwg )52( m eK)an

52

)52(5

52

)52(3

m

m

m

m

53 etIvibulmankMhusRtg;NakñúgkaredaHRsaysmIkar cUrrkkMhusenaH ? kMhusEdlvibulmanenARtg;karEcksmIkarCamYyktþa 52 m

BIeRBaHkñúgdMeNaHRsaysmIkareKminGacsRmYl b¤EckktþaEdlman GBaØat)aneTeRBaHvaGacnaM[)at;b¤ssmIkar . ^-plbUkR)aMcMnYnKt;bnþKñaes μInwg 520 . cUrrkR)aMcMnYnKt;enaH ? tag 4,3,2,1, xxxxx CaR)aMcMnYnKt;bnþKñaEdlRtUvrk eK)an 5204321 xxxxx

102

5105

520105

x

x

x

dUcenH CaR)aMcMnYnKt;EdlRtUvrk . 106,105,104,103,102

- 75 -


&-GayumIgsMesμInwg bIdgénGayusIuNaEdlCakUnrbs;Kat; . kalNasIuNamanGayues μInwgGayurbs;mþaynagsBVéf¶enH plbUkén GayuGñkTaMgBIresμInwg 112 qñaM .rkGayurbs;mIgsM ? tag x CaGayurbs;mIgsMbc©úb,nñ nig

3

x CaGayurbs;sIuNaCakUn

kalNasIuNamanGayues μImþaysBVéf¶enaHmIgsMnwgmanGayu 3

4x

tamsmμtikmμeK)ansmIkar 112)3

(3

4

xx

x

42

1123

8

x

x

dUcenHmIgsMmanGayu 42qñaM nigsIuNamanGayu 14qñaM . *-sUpatmanGayu 51 qñaM ehIyrsμImanGayu qñaM . 21

etIryHeBlb:un μanqñaMeTAmuxeToteTIbsUpatmanGayuesμInwg 2 dgén GayursμI ? tag x CacMnYnqñaMeTAmuxeTot eK)ansmIkar )21(251 xx eK)an 9x qñaM dUcenH 9qñaMeTAmuxeToteTIbsUpatmanGayuesμInwg 2 dgénGayursμI.

- 76 -

emeronTI7 vismIkardWeRkTI1manmYyGBaØat

- 77 -

lMhat; !-edaHRsayvismIkar k> 153 xx x> 52710 xx K> 1565 xx X> 1667 xx g> 75 xx c> 12)3(2 xx q> C> 2.475.03.2 m 05.53.14.4 t @-edaHRsayvismIkarrYcbkRsaycemøIyelIbnÞat;cMnYn k> x> 063217 a x K> 3 51 x X> 127

4

256

x

x

g> 3 4720 xx c> 63

1

m

q> 125

8

5

68

mm C> 54

22

54

63

xx #- edaHRsayvismIkarrYcbkRsaycemøIyelIbnÞat;cMnYn k> 2 237 xx x>

31

23

xxx

K> 3232

mmm X>

8

)1(33

4

1

mm


- 78 -

g> 4

18

3

191

6

)1(5

xxx

c> 4

13

8

)1(32

mm

q> 6

)3(11

3

7

2

13

4

13

xxxx

C> 157

5

21

13

25

9

25

2 xxx

$- edaHRsayvismIkarrYcbkRsaycemøIyelIbnÞat;cMnYn k> 73 x x> 55 x K> 5030 x X>

4

3

4

3x

g> 7

2

7

2 t c>

22

3

11

3 q

q> 155352 xxx C> yyy 12)12(3 Q> 5.05.1 x j> 200100 x d> 1232 xx z> 2565 mm D> 21287253 aaaa %-pldkrvag nigmYycMnYnFMCagplbUkrvag nig dgcMnYnenaH. 2 3 2

cUrrkcMnYnTaMgGs;EdlepÞógpÞat;bRmab;xagelI ?


dMeNaHRsay !-edaHRsayvismIkar k> 153 xx

2

3

64

513

x

x

xx

x> 52710 xx

2

38

12

128

75210

x

x

x

xx

K> 1565 xx

50

6155

x

xx

vismIkarKμancemøIy . X> 1667 xx 80 x KμancemøIy

- 79 -


- 80 -

g> 75 xx 20 x KμancemøIuy c> 12)3(2 xx

50

1262

x

xx

KμancemøIy . q> 2.475.03.2 m

5.1

45.33.2

75.02.43.2

m

m

m

C> 05.53.14.4 t

5.0

65.03.1

4.405.53.1

t

t

t

@-edaHRsayvismIkarrYcbkRsaycemøIyelIbnÞat;cMnYn k> 217 a

37

21

a

a


- 81 -

x> 063 x

23

6

63

x

x

x

K> 513 x

2

63

x

x

X> 1276 x 4

25 x

11

8

2433

2448285

48282524

x

x

xx

xx

g> 47203 xx

64

24

244

20473

x

x

x

xx


- 82 -

c> 63

1

m

19

181

m

m

q> 125

8

5

68

mm

10

202

406086

608640

m

m

mm

mm

C> 54

22

54

63

xx

8

6223

2263

x

xx

xx

#- eda bHRsayvismIkarrYc kRsaycemøIyelIbnÞat;cMnYn k> 2372 xx

9x

9

7232

x

xx


- 83 -

x> 3

12

3xx

x

13

6

613

26318

x

x

xxx

K> 3232

mmm

17

18

1817

181223

m

m

mmm

X> 8

)1(33

4

1

mm

29

332422

m

mm

g> 4

18

3

191

6

)1(5

xxx

2

3

32

211210

112210

3244361210

10

x

x

xx

xx

xxx


- 84 -

c> 4

13

8

)1(32

mm

5

7

75

22243316

m

m

mm

q> 6

)3(11

3

7

2

13

4

13

xxxx

3

5

159

6668115

66222867839

x

x

xx

xxxx

$-edaHRs nayvismIkarrYcbkRsaycemøIyelIb Þat;cMnYn k> 73 x 10x x> 55 x 10x K> 5030 x 0 2x


- 85 -

X> 4

3

4

3x

0x g>

7

2

7

2t

1

t c>

22

3

11

3 q

2

1q

q> 155352 xxx

2

2010

5 1555

x

x

xx

C> yyy 1212( )3

2

3

96

1236

y

y

yyy

Q> 5.05.1 x 1x


j> 200100 x 300x d> 1232 xx 1x

7m z> 265 m 5m

D> 753 21282 aaa a

- 86 -

2

1

24 109125

a

aa

nigmYycMnYnFMCagplbUkrvag nig dgcMnYnenaH. kcMnYnTaMgGs;EdlepÞógpÞat;bRmab;xag lI ?

a

%-pldkrvag 2 3 2

cUrr e tag x CacMn eK)an

YnEdlRtUvrk x23 x2

3

1x

13

x

emeronTI8 bøg;kUGedaen nig Rkab

lMhat; !-edayyk CargVas;ÉktaelIGkS½TaMgBIr cm1 oxx' nig oyy' edAcMnucEdlmankUGredaendUcteTA ³ 5,3: yxA 4,3: yxB 3,4: yxC 6,0: yxD 2,5: yxE 4,1: yxF 3,2: yxG 0,3: yxH 6,

2

1: yxI

- 87 -


@-KUsRtIekaN EdlmankMBUl ABC )3,6(;)2,8(;)5,4( CBA . #-KUsctuekaNEkg EdlmankMBUl ABCD )6,10(;)8,3( BA )5,5( C nig )4,7( D . $-kñúgtMruykUGredaeb yk CargVas;Ékta edAcMnucdUctetA ³ cm1

)0,3(:

)6,6(:

)4,1(:

)5,0(:

yxD

yxC

yxB

yxA

P¢ab; nig . etIGñksegáteXIjy:agdUcemþc ? BDACBC ,, AD

%-sg;RkabénsmIkarxageRkam ³ k> 53 xy x> 42 xy K>

2

12 yx X> 23 yx

g> yx 33 c> yx 1593

- 88 -


- 89 -

dMeNaHRsay !- edAcMnucEdlmankUGredaendUcteTA ³ 5,3: yxA 4,3: yxB 3,4: yxC 6,0: yxD 2,5: yxE 4,1: yxF 3,2: yxG 0,3: yxH 6,

2

1: yxI

2 3 4 5 6-1-2-3-4-5-6-7-8

2

3

4

5

6

7

-1

-2

-3

-4

-5

70 1

1

x

y

A

B

C

D

E

F

G

H

I


@-KUsRtIekaN EdlmankMBUl ABC )3,6(;)2,8(;)5,4( CBA .

2 3 4 5 6 7 8 9 10 11-1-2-3-4-5-6-7

2

3

4

5

6

-1

0 1

1

x

y

A

B

C

- 90 -


- 91 -

#-KUsctuekaNEkg EdlmankMBUl ABCD )6,10(;)8,3( BA )5,5( C nig )4,7( D . $-kñúgtMruykUGredaeb yk CargVas;Ékta edAcMnucdUctetA ³ cm1

)0,3(:)6,6(:

)4,1(:)5,0(:

yxDyxC

yxByxA

P¢ab; BDACBC ,, nig . etIGñksegáteXIjy:agdUcemþc ? AD

2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7

2

3

4

5

6

7

8

-1

-2

-3

-4

-5

0 1

1

x

yA

B

CD


- 92 -

2 3 4 5 6 7 8-1-2

2

3

4

5

6

-1

-2

0 1

1

x

y

C

D

A

B

%-sg;RkabénsmIkarxageRkam ³ k> 53 xy ebI 5,0 yx ebI

3

5,0 xy

2 3 4 5-1-2-3-4

2

3

4

5

6

-1

0 1

1

x

y


- 93 -

x> 42 xy ebI 4,0 yx ebI 2,0 xy

K>

2

12 yx ebI

2

1,0 yx ebI

4

1,0 xy

2 3 4 5-1-2-3-4

2

3

4

5

6

-1

0 1

1

x

y

2 3 4 5 6-1-2-3-4

2

3

-1

-2

0 1

1

x

y


- 94 -

X> 23 yx ebI 2,0 yx ebI 3

2,0 xy

g> yx 33 ebI 1,0 yx ebI 3,0 xy

2 3 4 5-1-2-3-4 6-5

2

3

4

5

-1

-2

0 1

1

x

y

2 3 4 5 6-1-2-3-4-5

2

3

4

5

-1

-2

0 1

1

x

y


c> yx 1593 ebI

5

3,0 yx

ebI 3,0 xy

2 3 4 5 6-1-2-3-4-5

2

3

4

5

-1

-2

0 1

1

- 95 -

x

y

emeronTI9 RbU)ab

lMhat; !-kñúgRbGb;mYymansársUkULa 24 RKab; kñúgenaHman 10RKab;mansñÚl ERkm 8RKab;KμansñÚl nigenAsl;mansñúlsENþk . sársUkULa ! RKab;RtUveRCIserIsedayécdnü . KNnaRbU)abEdlsársUkULa³ k>mansñÚlERkm x> mansñÚlsENþk K> minmansñÚlERkm. @-eKe)aHRKab;LukLak;mYyRKab . rkRbU)abénRBwtþikarN_xageRkam ³ k> e)aH)anelxess x> e)aH)anelxFMCag # K> e)aH)anelxEckdac;nwg % X> e)aH)anelxFMCag ! . #-rdæamaneRsameCIgBN’épÞemXcMnYn* BN’exovcMnYn & BN’sUkULa cMnYn !# nig BN’RkhmcMnYn^ .rdæaeRCIserIseRsameCIgmYyeday écdnü . KNnaRbU)abEdleRsameCIgman ³

- 96 -

emeronTI9 RbU)ab

k> BN’épÞemX x> BN’exov K> minEmnBN’sUkULa X> minEmnBN’sUkULa b¤ BN’Rkhm g> BN’épÞemX b¤ BN’exov . $-eKe)aHkak;mYycMnYnbIdg . k> KNnacMnYnkrNIGac x> KNnaRbU)abénRBwtþikarN_e)aHkak;)anxagrUbBIr nig xagelxmYy

- 97 -

emeronTI9 RbU)ab

dMeNaHRsay !-kñúgRbGb;mYymansársUkULa 24 RKab; kñúgenaHman 10RKab;mansñÚl ERkm 8RKab;KμansñÚl nigenAsl;mansñÚlsENþk . sársUkULa ! RKab;RtUveRCIserIsedayécdnü . KNnaRbU)abEdlsársUkULa³ k>mansñÚlERkm cMnYnkrNIGa

sbcMnYnkrNIRcP

42.012

5

24

10

x> mansñÚlsENþk cMnYnkrNIGa

sbcMnYnkrNIRcP

25.024

6

24

81024

K> minmansñÚlERkm cMnYnkrNIGa

sbcMnYnkrNIRcP

33.03

1

24

8

- 98 -

emeronTI9 RbU)ab

@-eKe)aHRKab;LukLak;mYyRKab . rkRbU)abénRBwtþikarN_xageRkam ³ k> e)aH)anelxess RBwtþikarN_Gac cMnYnkrNIGacesμI ^ . }6,5,4,3,2,1{

cMnYnkrNIRsb cMnYnkrNIRsbesμI # . }5,3,1{

cMnYnkrNIGasbcMnYnkrNIR

cP

5.06

3

x> e)aH)anelxFMCag # cMnYnkrNIRsb cMnYnkrNIRsbesμI # . }6,5,4{

cMnYnkrNIGasbcMnYnkrNIR

cP

5.06

3

K> e)aH)anelxEckdac;nwg % cMnYnkrNIRsb cMnYnkrNIRsbesμI!. }5{

6

1 cMnYnkrNIGa

sbcMnYnkrNIRcP

- 99 -

emeronTI9 RbU)ab

X> e)aH)anelxFMCag ! cMnYnkrNIRsb cMnYnkrNIRsbesμI % . }6,5,4,3,2{

6

5 cMnYnkrNIGa

sbcMnYnkrNIRcP

#-rdæamaneRsameCIgBN’épÞemXcMnYn* BN’exovcMnYn & BN’sUkULa cMnYn !# nig BN’RkhmcMnYn^ .rdæaeRCIserIseRsameCIgmYyeday écdnü . KNnaRbU)abEdleRsameCIgman ³ k> BN’épÞemX cMnYnkrNIGac 3461378 cMnYnkrNIRsb 8 .

17

4

34

8 cMnYnkrNIGa

sbcMnYnkrNIRcP

x> BN’exov cMnYnkrNIRsb 7 .

34

7 cMnYnkrNIGa

sbcMnYnkrNIRcP

- 100 -

emeronTI9 RbU)ab

X> minEmnBN’sUkULa b¤ BN’Rkhm

34

15

34

7

17

4P

g> BN’épÞemX b¤ BN’exov

34

15

34

7

17

4P

$-eKe)aHkak;mYycMnYnbIdg . k> KNnacMnYnkrNIGac RBwtþikarGac },,,,,,,{ TTTHTTTHTTTHTHHHTHHHTHHH cMnYnkrNIGacesμI 8 . x> KNnaRbU)abénRBwtþikarN_e)aHkak;)anxagrUbBIr nig xagelxmYy cMnYnkrNIRsb },,{ THHHTHHHT cMnYnkrNIRsbesμInwg # . 375.0

8

3 cMnYnkrNIGa

sbcMnYnkrNIRcP .

- 101 -

kn³kmμkarnibnæ nig eroberog μkarrtytbinitübec©kets · 2012. 6. 11. · emeronti9 rbu)ab 096...

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