Banco de Contenidos

 

_IHPOWQHNMN NO QMI AMWBEQ NO J_M^OCMBM OQA_OBM NO @EWCMAHÑI NO TWE@OQEWOQ NO OIQOÝMIVM CONHM O@TOC. TWMA^HAM NEAOI^O Q_TOWPHQMNM. GMIAE NO AEI^OIHNEQ HI@EWCMAHÑI JOIOWMB6 Histhtuahñi6 no onuamahñi gísham perAetzmfmy  aeepormthvm smtèbhto.   Iecgro nobHisthtute ostunhmito6 Cmrhe Esgorte Wuhz Aetzmfmy Amriè #6 74=:4>>14  74=:4>>14  Jrmne6 ^oraore gíshae Írom6 Cmtocítham AM^ONWÍ^HAE ^H^_BMW6 Gorby Fubhssm Wmxñi Ebhvm  Ebhvm   GMIAE NO AEI^OIHNEQ @_IAHÑI NOB HIQ^W_COI^E6 ^OCM NO BM _IHNMN =6 Wopmse no mrhtcètham ^OCM NO BM _IHNMN 76 Mbjogrm ^OCM NO BM _IHNMN 1 Oaumaheios ^OCM NO BM _IHNMN >6 ^rhjeiecotrãm ^rhjei ecotrãm AÑNHJE6 IHPOBOQ NO AEIEAHCHOI^E M 3 Ihvob no Ihvob no Woauorne.  Woauorne.   G 3 Ihvob no Ihvob no Aecproishñi.  Aecproishñi.   A 3 Ihvob no Ihvob no Mpbhamahñi.  Mpbhamahñi.  N 3 Ihvob no Ihvob no Miíbhshs.  Miíbhshs.  O 3 Ihvob no Ihvob no Ovmbumahñi.  Ovmbumahñi.  @ 3 Ihvob no Ihvob no Aromahñi. Ie.

IHPOB

AÑNHJE

AEI^OIHNE

_ihnmn ie. = Oxpeioitos y sus boyos roprosoitm, Aerrospeino m6 M bm epormahñi cmtocítham quo roprosoitm, oi `ercm mgrovhmnm, bm cubthpbhamahñi no `materos hjumbos so bo bbmcm petoiahmahñi. 

=

m

=.=

Bm petoiahmahñi, aece oxproshñi mbjogrmham, bm aei`ercmi bes shjuhoitos obocoites6 m 3 gmso c 3 oxpeioito g 3 petoiahm

Trhcorm boy6 Trenuate no petoiahms aei bm chscm gmso.

7

g

=.7

Ofocpbe6 (mmm). (mm)

 

 

Ter bm no`hihahñi no petoiahm so thoio6

Oforahahe6

Qojuinm boy6 Aeahoito no petoiahms aei bm chscm gmso

Ofocpbe6 Ter bm no`hihahñi no petoiahm so thoio6

1

a

=.1 Oforahahe6

^oraorm boy6 Tetoiahm no uim petoiahm Ofocpbe6 Ter bm no`hihahñi no petoiahm so thoio6

>

a

=.> ;

 

 

Oforahahe6

Aumrtm boy6 Tetoiahm no ui prenuate Ofocpbe6 (mg)1 (mg)1 3 mg x mg x mg (mg)1 3 m x m x m x g x g x g

 M1g1 Oforahahe6

?

a

=.?

]uhitm boy6 Aumine ui aeahoito so obovm m uim petoiahm

Ofocpbe6

0

a

=.0

Oforahahe6

 

 

Bes shjuhoitos amses so nonuaoi no bms boyos mitorheros. Oi bm nhvhshñi no petoiahms no bm chscm gmso y oxpeioito so mpbham bm sojuinm boy y rosubtm quo6

:

a

=.:

 Mpbhamine bm no`hihahñi no petoiahm6

Qo amiaobmi bes nhvhnoines y nhvhseros hjumbos y so thoio6

Oxpeioito iojmthve  Aece ob oxpeito os iojmthve, ob rosubtmne sorí uim `rmaahñi, neino bm petoiahm sorí ob noiechimner. Ter ofocpbe, sh c os peshthve, oiteiaos m-c 3=/mc.

<

g

=.<

Ofocpbes   ‑ 1-= 3 =/ 1.  ‑ 0-7 3 = / 07 3 =/10.  ‑ ?*8)== 3 >4?==.

(m*g)c3mc*gc. Oforahahe6  ‑ (?* 3 ?>*  3 >4>.  ‑ (71 * :)0 3 710* :0 3 =0=0.

Nhvhshñi no petoiahms aei gmso nh`oroito Qh so thoioi gmsos nh`oroitos pore aei hjumbos oxpeioitos so nhvhnoi bms gmsos y so cmithoio ob oxpeioito6 mc / gc 3 (m / g)c.

Ofocpbes   ‑ 141 / 71 3 (14/7)1 3 =?1.

=4

n

=.=4

 ‑ >>4> /  3 (>>4/ 3 ?,?>.

Oforahahe6

 

 

Qh bm petoiahm thoio aece oxpeioito uim `rmaahñi, ostm os rosuobtm mb trmis`ercmrbm oi uim rmãz i ‑ èshcm, neino ob iucormner so cmithoio aece oxpeioito y ob noiechimner roprosoitm ob ãinhao no bm rmãz6

 

==

n

=.== Oforahahe6

O fo forah rahahes ahes ros rosuo uobbtes   Oforahahe =  Ambaubmr bms epormaheios oitro bms petoiahms quo thoioi nh`oroitos gmsos6

=7

o

=.=7 7>* >> / * >> / )> / , y Oforahahe6

.

 

 

Añce sucmr y rostmr rmnhambos Aumine so lmgbm no sucmr y rostmr rmnhambos, r mnhambos, rombcoito so trmtm no sucmr e rostmr tèrchies aei rmãaos. Tmrm rombhzmr sucmr y rostmr rmnhambos socofmito socofmitos, s, be quo lmaoces os cmitoior ob rmnhamb socofmito y sucmr y rostmr bes aeo`hahoitos (iöcore quo ostí cubthpbhamine m bm rmãz). Ter ofocpbe, vmces m sucmr bes tros rmnhambos socofmitos nob mpmrtmne mitorher6

7?

n

=.7?

Cubthpbhamahñi y nhvhshñi no rmnhambos no nhsthite ãinhao

Tmrm oitoinor osto mpmrtmne thoios quo toior cuy abmre bm shjuhoito prochsm6

70

n

=.70

Ofocpbe6 

 

 

Cubthpbhamces oxpei oxpeioitos6 oitos6

`rmaahñi)

pebhieches

_i pebhieche pebhieche os  os uim sucm no vmrhes ceieches.

Qh tenes bes ceieches nob pebhieche sei ie socofmitos oitro sã, noahces quo ob pebhieche ostí oi `ercm ronuahnm. 

7:

m

=.7:

Amnm uie no bes ceieches quo `ercmi ui pebhieche so bbmcm tèrchie. Qh lmy ui ceieche no cmyer jrmne, èsto roahgo ob iecgro no tèrchie prhiahpmb,, y su aeo`hahoito so bbmcm aeo`hahoito prhiahpmb prhiahpmb.. Qh lmy ui ceieche shi pmrto bhtormb (ui prhiahpmb iöcore quo ie ostè cubthpbhamne per ihijuim botrm), èsto roahgo ob iecgro no tèrchie hinopoinhoito..  hinopoinhoito jrmne   nob pebhieche mb cmyer no bes Qo bbmcm jrmne jrmnes no sus ceieches.   _i pebhieche oi uim sebm vmrhmgbo so nhao ernoimne sh bes ceieches ostíi osarhtes no cmyer Qh ob pebhieche cís no uimm coier vmrhmgbojrmne. ie poismroces oi thoio èb aece

 

 

ernoimne.

 

Qucm no pebhieches oi lerhzeitmb Tmrm lmaor bms epormaheios oi lerhzeitmb prhcore osarhghces ui pebhieche y sojuhne oi bm chscm bãiom osarhghces ob etre quo vmces m sucmr e rostmr. Nospuès, mjrupmces tèrchies socofmitos. socofmitos . Ofocpbe6  

Ofocpbe6   Ofocpbe6 7<

g

=.7< .

Oforahahe6

.

 

 

Bm rostm no pebhieches aeishsto oi sucmr mb chiuoine ob epuoste nob sustrmoine. ( 7 x 1  + ?x - 1) ∗ ( 7x 1   - 1 x 7  +>x) 3 7 x 1  + ?x - 1 ∗ 7 x 1   + 1 x 7   ∗ > x   3 7 x 1   ∗ 7 x 1   + 1 x 7   + ?x∗ >x - 1 3 1 x 7  + x - 1 ( : x >   + > x 7   + :x + 7 ) - ( 0x 1  +

7

7+>

1

7

7

0

0

1

7

0

1

oforahahe6

(-7y ). (1x y) 3 (-7.1)x y  3 -0x y   (-:m g a ). (-7mga)3 =>m g a   (1?y  ). ( ‑  ‑yz   )3 (1?.-=)y z  3 -1?y z   (-mg ). (g a)3 (-=.=)mg a3 -mg a (>xyz ) (1x y )3 (>.1)x y z 3 =7x y z   1

1

1

>

1

?

1+=

>

1

1

1

7

1

?

1+=

1

0

1

1+7

7

1

=+7

>

>

1

?

=+1

1

1

>

1

 

 

Cubthpbhamahñi ceieche per pebhieche Tmrm aeithiumr aei bm cubthpbhamahñi no pebhieches,   so aebeam ob pebhieche aece pebhieches, cubthpbhamine y ob ceieche aece cubthpbhamner y sojuhnmcoito cubthpbhamces ob ceieche per amnm tèrchie nob pebhieche. Nogos toior oi auoitm6 Ambaubm ob prenuate shjuhoito6

1=

o

=.1= Wospuostm6  

Qebuahñi6  

Cubthpbhamahñi pebhieche per pebhieche Qo osarhgo ob cubthpbhamine y nogmfe ob cubthpbhamner y trmzms uim rmym per nogmfe no ostms nes bãioms.

17

o

=.17

 

 

Cubthpbhamahñi aei aeo`hahoitos `rmaaheimrhes Treaonhchoite6

Qo ernoimi bes pebhieches Qo osarhgoi ob cubthpbhamine y ob cubthpbhamner oi nes `hbms6 ob cubthpbhamine oi bm `hbm suporher y ob cubthpbhamner oi bm hi`orher. Qo trmzm uim bãiom lerhzeitmb nogmfe no ostms nes `hbms Qo cubthpbham amnm torchie nob cubthpbhamn c ubthpbhamner er per tenes bes tèrchies nob cubthpbhamine (toihoine oi auoitm

11

o

=.11

boy no bes shjies bes oxpeioito oxpeioitos) s)  bm  y bm boysonoosarhgo Amnm prenuate pmrthaubmr oi su rospoathvm `hbm nogmfe no bm bãiom lerhzeitmb y oi ob ernoi oi quo so o`oatumrei bes prenuates pmrahmbos6 oi bm prhcorm `hbm, ob prenuate nob prhcor tèrchie nob cubthpbhamner y tenes bes nob cubthpbhamine; oi bm sojuinm `hbm, ob prenuate nob sojuine tèrchie nob cubthpbhamner y tenes bes nob cubthpbhamine; oi bm toraorm `hbm, ob prenuate nob toraor tèrchie nob cubthpbhamner y tenes bes nob cubthpbhamine;... Bes tèrchies socofmitos so osarhgoi oi bm chscm aebucim Qo ronuaoi bes tèrchies socofmitos =

Nhvhshñi ceieche oitro ceieche Bm aumrtm epormahñi mrhtcètham os bm nhvhshñi, ob hivorse no bm cubthpbhamahñ cubthpbhamahñi. i. Bm nhvhshñi no pebhieches ie os tmi nh`oroito no bm nhvhshñi no iöcores. Ocpoaoces aei bm nhvhshñi no ui ceieche ui ceieche oitro etre ceieche, quo os bm gmso no nhvhnhr ui pebhieche oitro ui ceieche.

1>

g

=.1>

 

 

Nhvhshñi pebhieche oitro ceieche Pomces aece nhvhnhr ui pebhieche (quo puono toior nes e cís tèrchies) aei ui ceieche, quhoro noahr quo oi bm pmrto nob iucormner vmces m toior vmrhes tèrchies y oi bm pmrto nob noiechimner toinroces sebe uie. OF OCTBE H  

1?

a

=.1?

Oforahahe6

Nhvhshñi aei aeo`hahoitos `rmaaheimrhes pmrm penor rombhzmr ostm nhvhshñi nogoces no roaernmr bm rojbm no nhvhshñi no `rmaaheios oi mrhtcètham. Neino mb nhvhser bo nmces vuobtm os noahr oi iucormnes pmrm lmahm mrrhgm y ob noiechimner lmahm mgmfe. Oiteiaos ostm nhvhshñi so aeivhorto oi uim cubthpbhamahñi. Nhvhno6

10

a

=.10

Wospuostm6  Qebuahñi6 

Nhvhnhces bes aeo`hahoitos6 Oforahahe6

Nhvhno6

 

 

Wospuostm6 

Nhvhshñi pebhieche oitro pebhieche Bm nhvhshñi no pebhieches so puono o`oatumr no bm chscm cmiorm quo bm nhvhshñi mrhtcètham, aei jrminos iöcores, usmine ob mbjerhtce no Ouabhnos. Ter ofocpbe, nmnes bes iöcores 017 y 71, egtoijmces ob aeahoito per conhe nob mbjerhtce ahtmne, oste os6

Aecpregmahñi  Ter be tmite 017 3 71 x 7: + ==,

Ofocpbe6   Nhvhnhr 0x 7  + 1x + 7 oitro 7x + 1 Tmses m sojuhr6 =.

Qo nhvh nhvhno no ob prhcor tèrchie nob nhvhnhoine oitro ob  prhcor tèrchie nob nhvhser. 0x7 

1:

m

=.1:

7x

3 1

 x

7. 1.

1x 7x +

0x7 + 1x +

1

7

Oforahahe6

7

_ihnmn Ie. 7 Trenuate ietmgbo

1<

m

7.=

Amnm prenuate ietmgbo os uim `ñrcubm quo rosubtm no uim `materhzmahñi, aecpuostm per pebhieches no vmrhes tèrchies aece per ofocpbe ghieches e trhieches, bbmcmnes `materos.

 

 

Bes `materos sei bm gmso no uim petoiahm y thoioi ui oxpeioito. Aumine so cubthpbhami bes `materos, bes oxpeioitos nogoi sor sucmnes.

Oxhstoi vmrhms `ñrcubms no prenuate ietmgbo, uims sei cís usmnms quo etrms, nopoinhoine no bes pebhieches, y sei bms shjuhoitos6

Ghieche mb aumnrmne Os bm cubthpbhamahñi no ui ghieche per sã chsce, oxprosmnm oi `ercm no petoiahm, neino bes tèrchies sei sucmnes e rostmnes6 (m + g)7 3 (m + g) * (m + g). Ofocpbe = (x + ?)· 3 x· + 7 (x * ?) + ?·

18

g

7.7

(x + ?)· 3 x· + 7 (?x) + 7? (\ + ?)· 3 x· + =4x+ 7?. Oforahahe6 (>m + 7g) 3 (>m)7 + 7 (>m * 7g) + (7g)7 (>m + 7g) 3 m + 7g) 3 g7.

Trenuate no ghieches aeifujmnes Nes ghieches sei aeifujmnes aumine bes sojuines tèrchies no amnm uie sei no shjies nh`oroitos, os noahr, ob nob prhcore os peshthve y ob nob sojuine iojmthve e vhaovorsm. Qo rosuobvo obovmine amnm ceieche mb aumnrmne y so rostmi. Qu `ñrcubm os bm shjuhoito6

>4

g

7.1

(m + g) * (m ‑ (m  ‑ g)  g) Ofocpbe = (7m + 1g) (7m ‑ (7m  ‑ 1g)  1g) 3 >m7 + (-0mg) + (0 mg) + (-8g7) (7m + 1g) (7m ‑ (7m  ‑ 1g)  1g) 3 >m7 ‑ >m7  ‑ 8g7.  8g7. Oforahahe6

 

 

Trenuate no nes ghieches aei ui tèrchie aecöi Os uie no bes prenuates ietmgbos cís aecpbofes y peae uthbhzmnes perquo so trmtm no uim cubthpbhamahñi no nes ghieches quo thoioi ui tèrchie oi aecöi. Bm rojbm hinham be shjuhoito6 Ob aumnrmne nob tèrchie aecöi. Cís bm sucm bes tèrchies quo ie sei aecuios y buoje cubthpbhamrbes per ob tèrchie aecöi. Cís bm sucm no bm cubthpbhamahñi no bes tèrchies quo ie sei aecuios. Qo roprosoitm oi bm `ñrcubm6 (x + m) * (x + g)

>=

g

7.>

(x + 0) * (x + 8) 3 x7 + (0 + 8) * x + (0 * 8) (x + 0) * (\ + 8) 3 x7 + =?x + ?>. Oforahahe6

Tebhieche mb aumnrmne

>7

g

7.?

Oi osto amse oxhstoi cís no nes tèrchies y pmrm p mrm nosmrrebbmrbe, amnm uie so obovm mb aumnrmne y so sucmi  fuite aei ob negbo no bm cubthpbhamahñi cubthpbhamahñi no ui tèrchie aei etre; su `ñrcubm os6 (m + g + a)7 y ob rosubtmne no bm epormahñi os ui trhieche mb aumnrmne. Ofocpbe = (1x + 7y + >z)7 3 (1x)7 + (7y)7 + (>z)7 + 7 (0xy + =7xz + z)7 3 8x7 + >y7 + =0z7 + =7xy +7>xz + =0yz. Oforahahe6

Qucm no Ghieche mb auge Os ui prenuate ietmgbo aecpbofe. Tmrm nosmrrebbmrbe so cubthpbham ob ghieche per su aumnrmne, no bm shjuhoito cmiorm6 m. Tmrm ob ghieche mb auge no uim sucm6 Ob auge nob prhcor tèrchie, cís ob trhpbo nob aumnrmne nob prhcor tèrchie per ob sojuine. Cís ob trhpbo nob prhcor tèrchie, per ob sojuine mb aumnrmne. Cís ob auge nob sojuine tèrchie. (m + g)1 3 (m + g) * (m + g)7

>1

g

7.0

(m + g)1 3 (m + g) * (m7 + 7mg + g7) (m + g)1 3 m1 + 7m7g + mg7 + gm7 + 7mg7 + g1 (m + g)1 3 m1 + 1m7g + 1mg7 + g1.

Oforahahe6

Aeahoitos ietmgbos >>

g

7.:

Bes aeahoitos ietmgbos sei uims aumitms a umitms `ercubms ie tmi oxtoisms aece bes prenuates ietmgbos, no loale, bes aeahoitos ietmgbos quo ostunhmroces norhvmi no uim `ercm ospoaã`ham no uim nhvhshñi oxmatm neino sebe amcghmroces bes shjies pmrm toior nh`oroitos aeahoitos ietmgbos quo sh ghoi sei peams pore hcpertmito oi ob nosmrrebbe no bms cmtocíthams pmrm aurses pestorheros. Qhi cís quo noahr, aecoiaoces6 aecoiaoces6  

NH PH Q H ÑI O \M \MA^ A^M M

>?

a

7.<

_im nhvhshñi oxmatm os aumine su roshnue os aore y thoio bm `ercm joiormb6

 

 

Tore vmces m tecms ahortms nhvhsheios cís ietmgbos quo oiaeitrmces oi cualms íroms no cmtocítham aece tmcghèi no `ãsham. No bm soaahñi no  prenuates ietmgbos, ietmgbos,   tecmroces mbjuims `ñrcubms aece bm nh`oroiahm no aumnrmnes6

(

+

Qh no nosp spof ofmc mces es (

)(

+

)3

), toio toioce ces6 s6

NO@ H IH AHÑI AHÑ I NO _I _I AE AEAH OI^O IE^MGBO Bbmcmces aeahoitos ietmgbos mquobbms nhvhsheios oxmatms, os noahr, no roshnue aore quo so puono egtoior no `ercm nhroatm shi rosebvor e rombhzmr ihijöi thpe no nhvhshñi mbjogrmham. E^WEQ OFOCTBEQ TMW^HA_BMWOQ NO AEAHOI^OQ IE^MGBOQ

>0

a

7.8

Bes aeahoitos ietmgbos quo trmtmroces sei aece bes amses norhvmnes no bm nh`oroiahm no aumnrmnes y bm sucm y nh`oroiahm no auges, etres amses joiormbos sei6

e 

e 

AMQEQ NO BEQ AEAHOI^OQ IE^MGBOQ

>:

a

7.=4

Nob nhmjrmcm mitorher penoces oiaeitrmr > amses no bms aumbos mbjuims no obbms aei ahortms rostrhaaheios aucpboi aei bm no`hihahñi no aeahoito ietmgbo.  

Amse =6

os ui aeahoito ietmgbo.

 

 

 

Amse 76 y sebe sh

 

Amse 16 y sebe sh

 

os ui aeahoito ietmgbo sh os hcpmr. os ui aeahoito ietmgbo sh os pmr.

Amse >6

ostm nhvhshñi ie os

aeahoito ietmgbo

OQ^_NHE NO _I AEAHOI^O IE^MGBO

Ostunhe nob amse = 6 Mquã ie hcpertm sh ob

vmber no os pmr e hcpmr, ob aeahoito ietmgbo no bm `ercm6

><

n

7.==

Oste hinham quo bm nhvhshñi os oxmatm y per tmite, ostmces trmtmine aei ui aeahoito ietmgbo. Pomces ob roste no bes amses. Ostunhe nob amse 7 6 ostes amses sebe sei

mpbhamgbos pmrm vmberos neino os hcpmr,  per tmite, bm shjuhoito nhvhshñi os ui aeahoito ietmgbo6

>8

n

7.=7

Tmrm hcpmr, so aucpbo  per tmite, ob roshnue roshnue sorhm aaore ore (4)6

,

 

 

Ostunhe nob amse 16 Bm nhvhshñi no bm `ercm6

?4

n

7.=1

Qh os pmr so aucpbo roshnue quonmrãm msã6

, ob

Oste nocuostrm quo bm nhvhshñi no osto amse os ui aeahoito ietmgbo. Ostunhe nob amse >6 Bm shjuhoito nhvhshñi ie os ui aeahoito ietmgbo6

?=

n

7.=>

Efe6 Qh per M e G cethves ie smgos auíine os ui aeahoito ietmgbo  pmrm aumbquhor aumbquhor nhvhsh nhvhshñi ñi no bm `ercm joiormb6

?7

g

7.=? Qhcpbocoito mpbhamces ob toerocm nob roste pmrm hnoith`hamr sh bm nhvhshñi os ui aeahoito ietmgbo e ie. Ter ofocpbe, quoroces smgor sh bms shjuhoitos nhvhsheios sei aeahoitos ietmgbos6

 

 

=. 

7.  Pomces ob prhcor ofocpbe, hjumbmine ob nhvhser m aore, egtoioces ob vmber no

6

rocpbmzmine oi ob nhvhnoine roste os6

, ob

Nh`oroito no aore, per tmite, bm nhvhshñi nob amse = ie os ui aeahoito ietmgbo. Pomces ob sojuine ofocpbe, aece oi ob amse mitorher, hjumbmces m aore, ob vmber no

rocpbmzmine nhvhser

sorhm6

oi

ob

egtoioces egtoioces ob roste6

Qhjih`ham quo bm nhvhshñi nob sojuine ofocpbe os ui aeahoito ietmgbo.

NO QMWWEBBE QMWWEBBE NO _I AEAH AEAH O I^O IE^ IE^MGBO MGBO Mlerm vmces m nosmrrebbmr ob pebhieche aecpbote no ui aeahoito ietmgbo, hiabuhroces ob amse > oi ob nosmrrebbe pmrm quo toijmi aecpmrmthvm os aei ui roste nh`oroito nouim aorehnom no bms nhvhsheiosnonoañce bes amses mitorheros. Joiormbcoito ui aeahoito ietmgbo tecm bm shjuhoito `ercm6

?1

g

7.=0 Ob iöcore no tèrchies nob aeahoito no bm hjumbnmn nob  pebhieche os hjumb mb oxpeioito . Egsorvo bms shjuhoitos aeishnormaheios aeishnorm aheios auine quoroces nosmrrebbmr uim nhvhshñi no osto thpe y ostmr sojure no quo ob aeahoito aeithoio tenes bes tèrchies aecpbotes6  

Ob oxpeioito no gmso ‒ x– nhschiuyo nhschiuyo no = oi =.

 

Ob oxpeioito no gmso ‒ m– mucoitm no = oi = m pmrthr nob sojuine tèrchie.

 

 

   

Qh ob Nhvhser os ‒x∗m– tenes bes tèrchies nob aeahoitoo sei peshthves. aeahoit  x+m– bes shjies nob aeahoito sei Qh ob Nhvhser os ‒  ‒   x+m mbtorimnes +,∗,+,∗ +,∗,+,∗     ⋥

Pomces ob nosmrrebbe no bes > amses quo mamgmces no coiaheimr mitorhercoito.

Nosmrrebbe nob amse = 6 Osto amse shocpro os ui aeahoito ietmgbo y su nosmrrebbe os6

Oforahahe6

?>

a

7.=:

e 

e 

e 

e 

Nosmrrebbe nob amse 76 Osto amse sebe os

mpbhamgbo pmrm `ercm6

??

a

hcpmr y tecm bm shjuhoito

7.=<

Oforahahe6

e 

 

 

e 

Nosmrrebbe nob amse 16 Osto amse sebe os

mpbhamgbo pmrm aumine shjuhoito `ercm6

os pmr y tecm bm

Oforahahe6 ?0

a

7.=8 e  e  e 

e 

Nosmrrebbe nob amse > 6 Qh ghoi os ahorte quo ie so trmtm no ui aeahoito ietmgbo, no tenms cmiorms mquã to cuostre su nosmrrebbe, bm `ercm quo tecm ostm nhvhshñi os no bm shjuhoito `ercm6

?:

a

7.74

TW_OGM NOB NOQMWWEBBE NO _I AEAHOI^O IE^MGBO

Hjumbmine

ob

nhvhser

m

aore neino , mpbhamine ob cètene no Wu``hih mb nhvhnoine pore aecpbotmine aec pbotmine aores tmb aece so cuostro oi ob shjuhoito osquocm6

 

 

TW_OGM NOB NOQMWWEBBE NO _I AEAHOI^O IE^MGBO

Qebe pregmroces ob nosmrrebbe nob amse =, toijm oi auoitm quo ostm pruogm ie os uim nocestrmahñi mnoaumnm, bm cmiorm aerroatm no nocestrmrbe os per hinuaahñi. Mpbhamroces ob cètene no Wu``hih no bm nhvhshñi oxpbhamne oi bm soaahñi no nhvhshñi no nhvhshñi mbjogrmham pmrm mbjogrmham  pmrm ob am amse6 se6

?<

o

7.7=

@EWC_BM NOB ^OWCHIE JOIOWMB NO _I AEAHOI^O IE^MGBO

Qom ob shjuhoito aeahoito ietmgbo no bm `ercm6 ?8

a

7.77

Neino6

 

 

 

Trhcor

tèrchie6   Qojuine torchie6  

^oraor tèrchie6

 

Aumrte torchie6

Tmrm mquobbes amses neino ob shjie os iojmthve pmrm ob tèrchie oi bm peshahñi öihamcoito aumine `ercm

y

tèrchie

nob nosmrrebbe nob aeahoito, suaono ob nhvhser os no bm

nogo sor pmr, oxaopte pmrm ob prhcor quo shocpro os peshthve.

^OWCHIE AOI^WMB NO _I AEAHOI^O IE^MGBO Mitos no ambaubmr ob torchie aoitrmb no ui aeahoito ietmgbo, bes öihaes quo thoio ui öihae torchie aoitrmb sei mquobbes aeahoitos quo thoioi ob iöcore no tèrchies hcpmr, bm peshahñi nob torchie aoitrmb so osarhgo msã

y so ambaubm msã6

 

04

n

7.71  

 

Oforahahe6 Lmbbmr ob torchie aoitrmb no bm shjuhoito

 

Mlerm

 

 

y

, Ter bm

@MA^EWHVMAHEI ]uo porchto osarhghr aece cubthpbhamahñi nhalm oxproshñi.

0=

m

7.7>

Bes `materos e nhvhseros no uim oxproshñi mbjogrmham, sei bes tèrchies, ym somi iöcores y/e botrms, @materhzmr uim oxproshñi mbjogrmham (e sucm no tèrchies mbjogrmhaes), os ob preaonhchoite quo cubthpbhamnes oitro sã nmi aece prenuate bm prhcorm oxproshñi.  Msã, per ofocpbe, ofocpbe, sh cubthpbhamces cubthpbhamces m per m + g penoces vor què;

@mater aecöi ceieche. 

07

N

7.7?

Nogos hnoith`hamr ob `mater aecöi oitro tenes bes tèrchies no bm oxproshñi, y osarhghrbe aece aeo`hahoito no ui pmrèitoshs, oi ob aumb thoios quo osarhghr bes tèrchies rosubtmitos nospuès no nhvhnhr per ob `mater aecöi.

Ofocpbes;   m) @materhzmr x7y + x7z. 

 

 

g) @materhzmr  < c7 - =7 ci. 

Oforahahe6

Tebhieche e per mjrupmahñi no tèrchies.  Aumine oi uim @mater Aecöi oxproshñi mbjogrmham, ie tenes bes tèrchies thoioi mbjöi `mater oi aecöi, puonos rombhzmr uim mjrupmahñi oi pmrèitoshs no bes tèrchies quo sh thoioi, y msã penrís `materhzmr.

Ofocpbes; m) @materhzmr bm oxproshñi m c + g c + m i + g i.  

01

N

7.70

Oforahahe6

 

 

@MA^EW AEC_I TEW MJW_TMAHEI NO ^OWCHIE @materhzmr ob pebhieche mx + my + >x + >y per mjrupmahñi no tèrchies. mx + my + >x + >y 3(mx + my)(>x m y)(>x + >y)  Mjrupmine tèrchies. 3 m(x + y) + >(x + y) y) @materhzmine amnm jrupe per `mater aecöi. 3 (x + y)(m + >)

Ofocpbe =6 

0>

N

7.7:

m7 + mg + mx + gx   (m7 + mg) + (mx + g)  m(m + g) + x(m +g)   (m + g) (m +x)  

Oforahahe6

^rhieche aumnrmne por`oate  Ob trhieche aumnrmne por`oate os hjumb mb prenuate ietmgbo aumnrmne no ghieche e som, os prenuate no nes ghieches hjumbos6

0?

a

7.7<

Ofocpbe6   - @materhzmr > x7 ‑ =7  ‑ =7 x y + 8 y7 

 

 

Oforahahe6

AMQE OQTOAHMB ^rhieche aumnrmne por`oate per mnhahñi y sustrmaahñi Mjuhbmr, Grmve, Jmbbojes, Aorñi y Woyos (7448) hinhami quo ostm oxproshñi so trmtm no trmis`ercmrso oi ui (ghieche e trhieche), e neino so puono mpbhamr trhieche aumnrmne por`oate, so smam bm rmãz aumnrmnm nob prhcor y öbthce tèrchie.

Ofocpbe =6  =6 

00

g

7.78

m7 + 7m (m ‑ (m  ‑ g)  g) + (m ‑ (m ‑ g)  g) 7  Wmãz aumnrmnm aumnrmnm no m7  3 m Wmãz aumnrmnm aumnrmnm no (m ‑ (m ‑ g)  g) 7 3 (m ‑ (m  ‑ g)  g)   Negbo prenuate sus rmãaos  rmãaos   (7 \ m \ (m (m ‑ 7m(m  ‑ g)  g) (aucpbo)  ‑  g) 3 7m(m ‑ W6 (m + (m ‑ (m  ‑ g))  g)) 7  (m + m ‑ m ‑ g)  g) 3 (7m ‑ (7m ‑g) g) 7 

Nh`oroiahm no aumnrmnes Bm nh`oroiahm no aumnrmnes por`oates os hjumb mb prenuate ietmgbo sucm per su nh`oroiahm;

0:

A

7.14

Bm rojbm pmrm `materhzmr uim nh`oroiahm no aumnrmnes os; oxtrmor bm rmãz aumnrmnm mb prhcor y

 

 

mb sojuine aumnrmne, y so cubthpbham bm sucm no ostms rmãaos aumnrmnms per su nh`oroiahm.

Ofocpbe6   @materhzmr 7? ‑ 7? ‑ 10  10 x7: 

Oforahahe6

AMQE OQTOAHMB Nh`oroiahm no Aumnrmnes Tor`oates. Amse Ospoahmb. Wojbm pmrm `matermr uim nh`oroiahm no aumnrmnes; aumine uie e mcges aumnrmnes sei aecpuostes6 Qo oxtrmo bm rmãz aumnrmnm mb chiuoine y mb sustrmoine y so cubthpbham bm sucm no ostms rmãaos aumnrmnms per bm nh`oroiahm no nhalms rmãaos.

 

Ofocpbe =6

(m  7g)7  (x + y)7  

   7g) (xbm+sucm y) 3 per Wmãaos   Qo(mcubthpbham bm nh`oroiahm

0<

g

7.1=

W6 3 ((m  7g) + (x + y)) ((m  g)   (x + y))  (m  7g + x + y) (m 7g  x  y)  Ofocpbe 76 =0m=4  (7m7 + 1) 7  >m?  (7m7  + 1) 3 Wmãaos Qo cubthpbham bm sucm per bm nh`oroiahm W6 3 ((>m? + (7m7 + 1))( >m?  (7m7 + 1)) (>m? + 7m7 + 1)(>m?  7m7  1) Ofocpbe 16 

10(c + i)7  =7=(c  i)7 

 

 

0(c + i) ==(c  i)  3 Wmãaos Qo cubthpbham bm sucm per bm nh`oroiahm W6 3 ((0(c + i) + ==(c  i)) (0(c + i)  ==(c  i)) (0c + 0i + ==c ==i) (0c +0i  ==c + ==i) (=:c + ?i ) (?c +=:i)

AMQEQ OQTOAHMBOQ  AECGHIMAHEI NO BEQ AMQEQ HHH X HP

AÑCE @MA^EWHVMW6 Aumine sei aumtre tèrchies `ercmr ui trhieche aumnrmne por`oate oitro pmrèitoshs y `materhzmr per ob amse HHH, ob rosubtmne `materhzmr per ob amse HP Ospoahmb Aumine sei sohs tèrchies `ercmr nes trhieches aumnrmne por`oate y `materhzmr per ob amse HHH, ob rosubtmne `materhzmr per ob amse HP Ospoahmb Ofocpbe =6 m7 + 7mg + g7 - x7  (m7 + 7mg + g 7)  x7  (m + g) 7  x7  W 6 (m + g + x)(m + g  x)

08

g

7.17

Ofocpbe 76 =  m7 + 7mx  x7  =  (m7 + 7mx  x7)  =  (m  x)7  W6 (=  m + x) (= + m + x) Ofocpbe 16 =0m7  =  =4c + 8x7  7>mx  7?c7  (=0m7 7>mx + 8x7)  (= + =4c + 7?c7) (>m  1x) 7  (= + ?c) 7  W6 (>m  1x + ?c +=)(>m 1x ?c  =)

Auge no ghieche

:4

g

7.11

Ob auge no bm sucm no nes amithnmnos ((m + g) 1) os hjumb mb auge no bm prhcorm (m1) cís ob trhpbo prenuate nob aumnrmne no bm prhcorm per bm sojuinm (1m7g) cís ob trhpbo prenuate no bm

 

 

prhcorm per ob aumnrmne no bm sojuinm (1mg7) cís ob auge no bm sojuinm (g1).

Ofocpbe6   @materhzmr m1 + 1 m7 + 1 m + =. 

Qucm no auges. 

Bm `ñrcubm ies nhao quo, pmrm `materhzmr bm sucm no nes tèrchies obovmnes mb auge , so nosaecpeio oi nes `materos, neino; - Ob prhcor `mater, os bm sucm no sus rmãaos aöghams.

:=

g

7.1>

- Ob sojuine `mater, os ob aumnrmne no bm prhcorm rmãz, coies ob prenuate no bms nes rmãaos, cís ob aumnrmne no bm sojuinm rmãz.

Ofocpbe6   @materhzmr m1 + 7:. 

Oforahahe6

 

 

Nh`oroiahm no auges. 

Bm `ñrcubm ies nhao quo, pmrm `materhzmr bm nh`oroiahm no nes tèrchies obovmnes mb auge, so nosaecpeio oi nes `materos, neino; - Ob prhcor `mater, os bm nh`oroiahm no sus rmãaos aöghams. - Ob sojuine `mater, os ob aumnrmne no bm prhcorm rmãz, cís ob prenuate no bms nes rmãaos, cís ob aumnrmne no bm sojuinm rmãz.

Ofocpbe6  

a :7

7.1?

@materhzmr x1 ‑ =7?.  ‑ =7?. 

Oforahahe6

 

 

^rhieche no bm `ercm x7 + gx + a.  Bes trhieches ernoimnes no bm `ercm x7 + gx + a, nmi aece rosubtmne ob prenuate ietmgbo prenuate no ghieches;

=) @materhzmr x7 + 8 x + =>. 

:1

g

7.10

Oforahahe6

^rhieche no bm `ercm mx7 + gx + a.  Qo nh`oroiahmi no bes trhieches ostunhmnes ostunhmnes oi ob amse mitorher, oi quo ob prhcor tèrchie thoio per aeo`hahoito ui iöcore nhsthite no =.

Ofocpbe;   @materhzmr 74 x7 + :x ‑ :x ‑ 0.  0. 

:>

g

7.1:

Wospuostm6 74 x7 + :x ‑ :x ‑ 0  0 3 (>x + 1) (?x ‑ (?x ‑ 7).  7). Oforahahe6

 

 

^WHIECHE A_MNWMNE TOW@OA^E TEW MNHAHEI  X Q_Q^WMAAHEI

Osto os uie no bes amses ospoahmbos no `materhzmahñi. Aeishsto oi aeivorthr ui trhieche oi ui trhieche aumnrmne por`oate mnhaheiíinebo y sustrmyèinebo ui tèrchie Ob prhcor y toraor tèrchie thoio quo sor aumnrmnes por`oates. X ob egfothve os lmaor quo ob sojuine tèrchie som ob negbo nob prenuate no bms rmãaos no oses aumnrmnes. Osto preaose so bbmcm ‒aecpbocoitmr aumnrmnes–  Ofocpbe =6 m> + m7 + =  =  + m7 

7

 m

 

m> + 7m7+ =  m7 

:?

g

7.1<

(m> + 7m7+ =)  m7  (m7 + =)7  m7  W6 (m7+ m + =) (m7 ‑  ‑ m  m + =)  =)  

 

 

AMQE OQTOAHMB  @MA^EWMW _IM Q_CM NO NEQ A_MNWMNEQ Oi joiormb uim sucm no nes aumnrmnes ie thoio nosaecpeshahñi oi `materos rmaheimbos, os noahr, `materos oi quo ie lmym rmãz, pore lmy sucms no aumnrmnes quo, sucíinebos y rostíinebos uim chscm amithnmn, puonoi bbovmrso mb amse mitorher y nosaecpeiorso. 

:0

g

7.18

Ofocpbe =6 x>+ 0>y>  x> + 0>y>  + =0x7y7  x> + =0x7y7 + 0>y>  (x> + =0x7y7 + 0>y>)

 =0x

7 7

y 7 7  =0x y    =0x7y7 

(x7 + xy)   (x7 + >xy + xy +

4

m? + = 3 m>   ‑ m ‑ m1 + m7   ‑ m ‑ m + =  =  m + =  = 

Ofocpbe 76 c:   ‑ i ‑ i: 

c:   ‑ i ‑ i:  3 c0 + c?i + c>i7 + c1i1 + c7i>+ ci? + i0  c ‑  i  ‑ i

 

 

Ofocpbe 16 

x: + =7   ‑ 7x ?  + >x >   ‑