Guia de Aprendizaje #5 Medidas de Dispersión III Medio

 

Iuåk fc trkdkhn B¿3/ Ektceëgk ‑Ecf`fks fc f`spcrs`÷b― Wciubfk Ctkpk /7Ecf`n ^^^^^ _rnjcsnr8 Pnbktmkb Jucbzka`fk ‗ Cfugkfnrk/Cspcg`ka`stk 8 ^^^^^^ Jcgmk8 Bnedrc Cstuf`kbtc8 ^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^  

Bnedrcs Kpcaa`fn _k _ktcrbn

Kpcaa`fn Ek Ektcrbn

Sb`fkf ;8 Ca usn fc fktns cstkfåst`gns cstkfåst`gns y fc enfcans prndkd`aåst`gns pkrk ak tnek fc fcg`s`nbcs NK B¿48 Vnekr fcg`s`nbcs cb s`tukg`nbcs fc `bgcrtczk quc `bvnaugrcb ca kbëa`s`s fc fktns cstkfåst`gns gnb ecf`fks fc f`spcrs`÷b y prndkd`a`fkfcs gnbf`g`nbkacs. Ndhcvn Vrkbsvcrska/Kgtufcs8  Vrkbsvcrska/Kgtufcs8   Vnekr fcg`s`nbcs jubfkecbtkfks cb cv`fcbg`k cstkfåst`gk y/n cb ak

cvkaukg`÷b fc rcsuat cvkaukg`÷b rcsuatkfns kfns ndtcb`fns k pkrt`r fc ub enfca enfcann prndkd`aåst prndkd`aåst`gn. `gn. Kriuecbtkr, ut`a`zkbfn ut`a`zkbfn acbiuk acbiukhc hc s`ed÷a`gn y f`jcrcbtcs rcprcscbtkg`nbcs pkrk hust`j`gkr ak vcrkg`fkf n jkascfkf fc ubk gnbhcturk, y cvkaukr ca kagkbgc y ans aåe`tcs fc ans kriuecbtns ut`a`zkfns. Ndhct`vn fc ak gaksc 8 Gneprcbfcr y kpa`gkr aks ecf`fks fc f`spcrs`÷b cb ak tnek fc fcg`s`nbcs. @bstrugg`nb @bstr ugg`nbcs8 cs8 Ack ktcbtkecbtc ca gnbtcb`fn fc ak ub`fkf y aucin rcka`gc aks kgt`v`fkfcs fc kpa`gkg`÷b  prnpucstks.

Ecf`fks fc f`spcrs`÷b Aks ecf`fks fc f`spcrs`÷b fctcre`bkb gukb gcrgkbns n achkbns cstëb ans fktns fc ub vkanr gcbtrka, rcspcgtn k ak ecf`k kr`teàt`gk. Vked`àb `bf`gkb ca irkfn fc vkr`kd`a`fkf fc ans fktns. Cb cstk iuåk trkdkhkrcens aks s`iu`cbtcs8

Aks ecf`fks fc tcbfcbg tcbfcbg`k `k gcbtrka (EVG) y ecf`fks ecf`fks fc f`spcrs`÷b f`spcrs`÷b (EFF) bns s`rvcb pkrk gkrkgtcr`zkr ubk irkb gkbt`fkf fc `bjnrekg`÷b gnb pngns y d`cb fcj`b`fns vkanrcs. Aks EVG snb `fcks sndrc ak rcprcscbtkt`v`fkf fc ans fktns. Ak fcsv`kg`÷b ecf`k y cstëbfkr, prcscbtk f`jcrcbg`ks euy pcqucûks cb su gëaguan. Aks ecf ecf`fk `fkss fc f`s f`spcrs pcrs`÷b `÷b pcre`tc pcre`tcbb gnbs`fc gnbs`fcrkr rkr quà tkb tkbtk tk gnbj`kd gnbj`kd`a `a`fk `fkff pnfcens pnfcens tcbcr tcbcr cb ak rcprcscbtkt`v`fkf fc ubk ecf`fk fc rcsuecb sndrc ub gnbhubtn fc fktns. Ak cstkfåst`gk cs ubk fc aks ërcks fc ak ektceët`gk eës ut`a`zkfks cb ak kgtuka`fkf8 fcsfc ca trkdkhn g`cbtåj`gn mkstk ca j`bkbg`crn, pkskbfn pnr aks fcg`s`nbcs sng`kacs. ;

 

kaa prnjcsnr  prnjcsnr   Kyufk k

Ca gnaci`n fc Wpr`bij`caf ntnrikrk ubk dcgk fc ektråguak  pkrk pkrk ak ub`vcrs`fkf fc Wpr`bij`caf ka cstuf`kbtc guyn ducb rcbf`e`cbtn sc mkyk ekbtcb`fn pnr ekynr t`cepn cb ca øat`en scecstrc fc 6¿ ecf`n. ecf `n. _kr _krkk gka gkagua guakr kr ca echnr echnr prne prnecf` cf`nn snan sc gnbs`f gnbs`fcrkr crkrnb nb kaiubks ks`ibkturks. Ans echnrcs cstuf`kbtcs fc ak prneng`÷b jucrnb Mnecrn (kbtcs fc ectcrsc ca grky÷b cb ca gcacdrn) y Ekric. Ak ecf`k kr`teàt`gk ( x¶ ) fc gkfk ubn fc caans juc :,7. W` snan snan ubn ubn  fc fcdc dc scr scr ca caci ci``fn ¾qu ¾qu`à `àb b ikbkr ikbkrk k ak dcgk> dcgk>  Aks gka ka``j` j`ggkg kg``nbc bcss quc ndtuv`cr crnnb ju juccrnb aks s`iu`cbt btccs8 Acbiukhc Mnecrn Ekric

   

Ektceët`gk

M`stnr`k 9,?

 

:,7

3,=

 

:,6

:,0

 

3,?

:,4

 

:,=

 

G`cbg`ks

_krk pnfcr _krk pnfcr kyufk kyufkrr ka prn prnjc jcsnr snr fc cstns cstns fns ka kaue uebn bnss vk vken enss k ut ut`a `a`z `zkr kr ak akss ecf` ecf`fk fkss fc f` f`spc spcrs` rs`÷b, ÷b, kbka`zkrcens kbka`z krcens gkfk ubk fc caaks y ka j`bka skgkrcens ubk gnbgaus`÷b pkrk kyufkr ka prnjcsnr cb su fcg`s`÷b fcg`s`÷b j`bka.

Ca Tkbin Ca Tkbin ( T ) gnrrcspnbfc k ak f`jcrcbg`k cbtrc ca ekynr y ca ecbnr fc ans fktns fc ak f`str`dug`÷b. Cstk ecf`fk `bf`gk fc ka kaiu iubk bk ekbcr kbcrkk guëb guëb f` f`sp spcr crsn snss cs csttëb ans fkt fktns fc ak f`str`dug`÷b. Ca Tkbin fc ub gnbhubtn fc fktns bueàr`gns, sc gkaguak gnen ak f`jcrcbg`k cbtrc ca ekynr y ca ecbns vkanr fc ak f`str`dug`÷b fc fktns.  T 5fktnekynr ∔ fktnecbnr

Bntk8 _nr gurns kbtcr`nrcs yk skdcens quc8 Ca TKBIN, s`rvc pkrk fctcre`bkr ca tkekûn fc gkfk `btcrvkan cb ubk tkdak fc jrcgucbg`ks. Bn cs ubk ecf`fk euy s`ib`gkvk, yk quc àstc bns `bf`gk, guëb f`spcrsns sc cbgucbtrkb ans fktns cbtrc ans vkanrcs fc ans cxtrcens.

Cb bucstrn gksn pkrt`guakr ca rkbin sc gkaguak fc ak s`iu`cbtc jnrek8 Kauebn

F`jcrcbg`k cbtrc fktn ekynr y ecbnr

Mnecrn Ekric

   

Tkbin

9,? ∔3,?54,?

 

T 54,?

:,= ∔3,=5;,?

 

T 5;,?

Gnbgaus`÷b8 Gnen ca vkanr fca Tkbin fc aks bntks fc Mnecrn cs ekynr quc ca fc Ekric, pnfcens fcg`r quc sus gka`j`gkg`nbcs snb eës f`spcrsks. _nr an tkbtn, scråk ca eës kptn Ekric pkrk ikbkr ak dcgk pnr ekbtcbcr ub ducb rcbf`e`cbtn, pcrn tnfkvåk bn pnfcens fcg`r qu`cb rckaecbtc sc aacvk ak dcgk. Mkd`a`fkf8 Tcsnavcr prndaceks/Kriuecbtkr y Gneub`gkr  4

 

Kgt`v`fkf8 Gkaguak ca rkbin fc gkfk ubn fc ans s`iu`cbtcs cstuf`kbtcs, aks gka`j`gkg`nbcs snb fc ? k ;?. Kauebn

Gka`j`gkg`÷b ;

Gka`j`gkg`÷b 4

Gka`j`gkg`÷b 7

Gka`j`gkg`÷b 6

Kadcrtn 

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Dcktr`z 

;?

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;?

4

Gkrans 

:

9

0

;?

;. Tca Tcaacb acbkk ak ttkda kdakk gka gkagua guakbfn kbfn ca rkbin rkbin.. Kauebn

F`jcrcbg`k

Tkbin

Kadcrtn  Dcktr`z  Gkrans 

4. ¾[uà gnbgau gnbgaus`÷b s`÷b ppucfcs ucfcs skgkr gnb ccsns sns fk fktns tns quc ndtuv`stc> ndtuv`stc>

¾Bcgcs`tks vcr ca v`fcn fc ak ektcr`k> Csgkbck ca s`iu`cbtc g÷f`in [T pkrk quc vucavks k vcr ca chcepan.

Cbjngk ngk ak gëe gëekrk krk  fca e÷v e÷v`a `a n tkd tkdact actk k mk mkg`k g`k ca g÷f g÷f`in `in qu quc c qu qucrc crcens ens Cbj gkpturkr. Tcgnrfkr cstkr gnbcgtkfn k `btcrbct fcsg`jrkrë.. Ak kpa`gkg`÷b cbgukfrkrë ca g÷f`in y fc ekbcrk kutneëgk an fcsg`jrkrë Cb gk gksn sn fc bn mk mkgc gcra ran n fc fcsg sgkr krik ikrr ub ubk k kp kpp p fc ac acgt gtnr nr fc g÷ g÷f` f`in in [T (gukaqu`crk fc kppstnrc). Fcpcbf`cbfn fca gnbtcb`fn ka quc qu`crk aacvkrbns sc bns njrcgcrëb f`jcrcbtcs npg`nbcs8 `r k ak pëi`bk wcd, uskr PnuVudc pkrk vcr ub våfcn...

A`bl8 mttps8//ynutu.dc/q3dYWV@kZ?i>t54 Vked`àb pucfcs rcv`skr ak ektcr`k cb tu a`drn fc ektceët`gk cb ak pëi`bk ;;

7

 

Fcsv`kg`÷b Ecf`k Ak fcsv`kg`÷b ecf`k ( F ) rcprcscbtk ca ekynr n ecbnr kachke`cbtn fc ub fktn gnb rcspcgtn k ak ecf`k  ¶ ‑  pnr kr`teà kr` teàt`g t`gkk ‑ x  ,pnr an tkbtn ak  F E  sc fcj`bc gnen ak ecf`k kr`teàt`gk fc aks fcsv`kg`nbcs kdsnautks rcspcgtn k ak ecf`k kr`teàt`gk y pkrk gkaguakr cstks fcsv`kg`nbcs ecf`ks ut`a`zkrcens ak s`iu`cbtc jnreuak.  E 

b

¾ x ∔ x¶ ∭¾ ∛ 5 `

` ;

b

 

¾

Cb bucstrn gksn pkrt`guakr fc Mnecrn y Ekric yk skdcens quc ak ecf`k kr`teàt`gk fc kedns kauebns cs fc . W` gk gkag agua uake kens ns ak f` f`jc jcrc rcbg bg`k `k fc ub ubkk bn bntk tk gn gnbb ak ec ecf` f`kk Bntk8 Ca vkanr kdsnautn ‑― `bf`gk f`stkbg`k cbtrc pnr cbfc bubgk cs bcikvn. Chcepan8 yk quc quc bn bn cx`stc f`stkbg`ks bcikvks.

:,7

̃ ̃ . ̃ ) tcbfrcens ak fcsv`kg`÷b fc ak bntk gnb rcspcgtn k  x kr`teàt`gk ( x̃

̃ 5:,7  sc gkaguakb gnen Aks fcsv`kg`nbcs fc tnfks aks bntks tkbtn fc Mnecrn y Ekric, gnb rcspcgtn k  x̃ sc `bf`gk k gnbt`bukg`÷b

K gnbt`bukg`÷b, sc gkaguak ak fcsv`kg`÷b ecf`k _krk Mnecrn8 Acbiukhc Gka`j`gkg`nbcs fc Mnecrn

¾ x ∔ x¶ ∭¾

 

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b

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|:,0 ∔:,7|5?,:   |3,? ∔:,7|5;,7   |9,? ∔:,7|5?,9   |:,7 ∔:,7|5?  F E 5

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Ektceët`gk

?,: + ;,7 + ?,9 + ? 6

5

4,: 6

5?,:3

 Fc `iuka jnrek (kbëanikecbtc) sc rcka`zk ca fc Ekric

Vc `bv`tn k gnrrndnrkr quc ak fcsv`kg`÷b ecf`k fc Ekric  F E 5¾ ?,7 Gnbgaus`÷b8 6

 

Kmnrk gnb ak `bjnrekg`÷b fc aks  F  fc kedns pnfcens gnbgau`r kmnrk quc Ekric, prcscbtk ubk echnr   pns`g`÷b fc sus bntks rcspcgtn fc su ecf`k kr`teàt`gk     ̃, kqucaan pnrquc ?,7 cs ecbnr ?,:3< fkbfn ak `eprcs`÷b quc sus bntks bn sc cbgucbtrkb tkb kachkfks fc su prnecf`n k f`jcrcbg`k gnb an quc sugcfc gnb Mnecrn, pcrn tnfkvåk bn pnfcens fcg`r qu`cb rckaecbtc sc aacvk ak dcgk.  E 

Mkd`a`fkf8 Tcsnavcr prndaceks/Kriuecbtkr y Gneub`gkr   pkrk aks bntks fc Kadcrtn, Dcktr`z y Gkrans quc sc eucstrk cb ak tkdak Kgt`v`fkf8 Cbgucbtrk ca  F E  pkrk Gka`j`gkg`÷b ;

Kauebn

Gka`j`gkg`÷b 4

Gka`j`gkg`÷b 7

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;. Tc Tcaa aacb cbkk ak ak tkd tkdak ak.. Kadcrtn Gka`j`gkg`÷b

Gka`j`gkg`÷b ;

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Gka`j`gkg`÷b 4

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Gka`j`gkg`÷b ;

Gka`j`gkg`÷b

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Gkrans

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4. ¾[uà gnbgau gnbgaus`÷b s`÷b pu pucfcs cfcs sk skgkr gkr ka gnepkrkr gnepkrkr aks fcsv`kg fcsv`kg`nbcs `nbcs ecf`k ecf`ks> s>

¾Bcgcs`tks vcr ca v`fcn fc ak ektcr`k> Csgkbck ca s`iu`cbtc g÷f`in [T pkrk quc vucavks k vcr ca chcepan.

gëekrk fca e÷v`a n tkdactk mkg`k ca g÷f`in quc qucrcens Cbjngk ak gëekrk fca gkpturkr. Tcgnrfkr cstkr gnbcgtkfn k `btcrbct Ak kp kpa` a`gk gkg` g`÷b ÷b cb cbgu gukf kfrk rkrë rë ca g÷ g÷f` f`in in y fc ekbc ekbcrk rk ku kutn tneë eëg gk k fcsg`jrkrë.. Cb gksn fc bn mkgcran fcsgkrikr ubk kpp fc acgtnr fc an fcsg`jrkrë g÷f`in [T (gukaqu`crk fc kppstnrc). Fcpcbf`cbfn fca gnbtcb`fn ka quc qu`crk aacvkrbns sc bns njrcgcrëb f`jcrcbtcs npg`nbcs8 `r k ak pëi`bk wcd, uskr PnuVudc pkrk vcr ub våfcn...

A`bl8 mttps8//ynutu.dc/PDCLnhJ6C06>t50 Vked`àb pucfcs rcv`skr ak ektcr`k cb ak pëi`bk ;4 fc tu a`drn fc ektceët`gk

Zkr`kbzk y Fcsv`kg`÷b Cstëbfkr

Ak vkr`kbzk pndakg`nbka ( χ 4) y ak fcsv`kg`÷b cstëbfkr n tåp`gk ( χ ) pcre`tcb gukbt`j`gkr ak f`spcrs`÷b, cs fcg`r, `bf`gkb ak f`spcrs`÷b n scpkrkg`÷b fc ub gnbhubtn fc fktns. Ak vkr`kbzk gnrrcspnbfc k ak ecf`k b kr`teàt`gk fc ans gukfrkfns fc aks fcsv`kg`nbcs fc ans  fktns. E`cbtrks quc ak fcsv`kg`÷b cstëbfkr cs ak rkåz fc ak vkr`kbzk.

Ak vkr`kbzk sc gkaguak fc ak s`iu`cbtc ut`a`zkbfn aks s`iu`cbtc jnreuak8  

b

4

( x ∔ x¶ ) ∛ 5 `

4

χ 

5

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b

Ak fcsv`kg`÷b cstëbfkr sc gkaguak ecf`kbtc aks s`iu`cbtc jnreuak8

χ 5

∘

b

4

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:

 

Mky quc gnbs`fcrkr quc e`cbtrks ecbnr sck ca vkanr fc ak vkr`kbzk n fcsv`kg`÷b cstëbfkr, s`ib`j`gk quc ca gnbhubtn fc fktns cb gnbs`fcrkg`÷b cs eës mneniàbcn. _nr ntrn akfn, s` ca vkanr fc f`gmk vkr`kbzk n fcsv`kg`÷b cstëbfkr jucrk eës irkbfc, s`ib`j`gk quc mky ekynr f`spcrs`÷b, cb gnbscgucbg`k, ca gnbhubtn fc fktns cs eës Mctcrniàbcn.

W`ikens gnb bucstrns cstuf`kbtcs Mnecrn y Ekric gnb sus bntks, yk skdcens quc sus prnecf`ns  x¶ 5:,7 Gkaguakrcens ak vkr`kbzk y fcsv`kg`÷b cstëbfkr pkrk Mnecrn, pkrk mkgcran aacbkrcens ak s`iu`cbtc tkdak. Acbiukhc

Gka`j`gkg`nbcs fc Mnecrn

( x ∔ x¶ ) `

:,0

Ektceët`gk

 

M`stnr`k

3,?

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9,?

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G`cbg`ks

 

( 9,?∔ :,7 )5?,9

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(pucfc scr bcikt`vn) 4

( x ∔ x¶ ) `

¾

¾

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Zkr`kbzk b

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∶ akvkr`kbzkcs

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b

Fcsv`kg`÷b cstëbfkr  χ 5

5

4

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4

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b

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6 ∶ ak fcsv`kg fcsv`kg`÷b `÷b cstkb cstkbfër fër cs 5?,90 6

5?,90

b

Wc rcka`zk Kbëanikecbtc pkrk Ekric

Ak vkr`kbzk fc Ekric cs fc8 Ak fcsv`kg`÷b cstëbfkr fc Ekric cs fc8

4

χ 

 

5?,;7

χ 5?,7: 

¡_ucfcs

gneprndkrak! Gnbgaus`÷b8

Gnen pnfcens vcr quc ca vkanr fc ak fcsv`kg`÷b cstëbfkr fc aks bntks fc Ekric, cs ecbnr quc ka fc Mnecrn, cbtnbgcs, pnfcens fcg`r quc aks gka`j`gkg`nbcs fc Ekric, cstëb eës gcrgkbks k su ecf`k ̃ 5:,7 ) y snb cbtnbgcs ecbns f`spcrsks s`b auikr k fufks. Cb gnbscgucbg`k, ca eës `bf`gkfn kr`teàt`gk ( x̃  pkrk ikbkrsc ak DCGK DCGK FC EK EKVT VTÅG ÅGSA SAK K quc ntnrik ca gnaci`n cs Ekric, yk quc sus gka`j`gkg`nbcs guepacb gnb mkdcr ekbtcb`fn ub ducb rcbf`e`cbtn y snb ecbns f`spcrsks quc aks bntks fc Mnecrn, tcb`cbfn kedns ca e`sen prnecf`n (:,7 ) . ¾Bcgcs`tks vcr ca v`fcn fc ak ektcr`k> Csgkbck ca s`iu`cbtc g÷f`in [T pkrk quc vucavks k vcr ca chcepan.

9

 

Cbjngk ak gëekrk fca e÷v`a n tkdactk mkg`k ca g÷f`in quc qucrcens gkpturkr. Tcgnrfkr cstkr gnbcgtkfn k `btcrbct Ak kpa`gkg`÷b cbgukfrkrë ca g÷f`in y fc ekbcrk kutneëgk an fcsg`jrkrë. Cb gksn fc bn mkgcran fcsgkrikr ubk kpp fc acgtnr fc g÷f`in [T (gukaqu`crk fc kppstnrc). Fcpcbf`cbfn fca gnbtcb`fn ka quc qu`crk aacvkrbns sc bns njrcgcrëb f`jcrcbtcs npg`nbcs8 `r k ak pëi`bk wcd, uskr PnuVudc pkrk vcr ub våfcn...

A`bl8 mttps8//ynutu.dc/PDCLnhJ6C06>t50 Vked`àb pucfcs rcv`skr ak ektcr`k cb ak pëi`bk ;7 fc tu a`drn fc ektceët`gk

Mkd`a`fkf8 Tcsnavcr prndaceks/Kriuecbtkr y Gneub`gkr  Kgt`v`fkf8 Gnb aks bntks fc ans cstuf`kbtcs Kadcrtn, Dcktr`z y Gkrans quc sc eucstrkb k gnbt`bukg`÷b Kauebn

Gka`j`gkg`÷b ;

Gka`j`gkg`÷b 4

Gka`j`gkg`÷b 7

Gka`j`gkg`÷b 6

Kadcrtn 

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Dcktr`z 

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Gkrans 

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0

;?

;. Gka Gkagua guakr kr ca vkanr fc ak fcsv`kg`÷ fcsv`kg`÷bb cstëbf cstëbfkr kr y vkr` vkr`kbzk kbzk pkrk pkrk gkfk ubn fc caans. caans. Tcaac Tcaacbkbf bkbfnn ak tkdak tkdak fc gkfk ubn fc caans Kadcrtn Gka`j`gkg`nbcs

Acbiukhc

Ektceët`gk

M`stnr`k

G`cbg`ks

=

=

=

=

Acbiukhc

Ektceët`gk

M`stnr`k

G`cbg`ks

;?

;?

;?

4

( x ∔ x¶ ) `

(pucfc scr bcikt`vn) 4

( x ∔ x¶ ) `

(s`ceprc pns`t`vn)

Zkr`kbzk b

4

( x ∔ x¶ ) 4

χ 

` 5; 5∛

`

b

Fcsv`kg`÷b cstëbfkr  χ 5

∘

b

4

( x ∔ x¶ ) ∛ 5 `

` ;

b

Dcktr`z Gka`j`gkg`nbcs

( x `∔ x¶ ) (pucfc scr bcikt`vn)

( x ∔ x¶ )

4

`

(s`ceprc pns`t`vn)

=

 

Zkr`kbzk b

4

( x ∔ x¶ ) ∛ 5 `

4

χ  5

` ;

b

Fcsv`kg`÷b cstëbfkr  χ 5

∘

b

4

( x ∔ x¶ ) ∛ 5 `

` ;

b

Kadcrtn Gka`j`gkg`nbcs

Acbiukhc

Ektceët`gk

M`stnr`k

G`cbg`ks

:

9

0

;?

( x ∔ x¶ ) `

(pucfc scr bcikt`vn) 4

( x ∔ x¶ ) `

(s`ceprc pns`t`vn)

Zkr`kbzk b

4

( x ∔ x¶ ) ∛ 5 `

4

χ 

5

` ;

b

Fcsv`kg`÷b cstëbfkr  χ 5

∘

b

4

( x ∔ x¶ ) ∛ 5 `

` ;

b

4. ¾[uà ppucfc ucfcss gnbg gnbgau` au`rr fc ans ffktn ktnss ndtcb`f ndtcb`fns> ns>

0