Algebra i Bim

7/17/2019 Algebra i Bim

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ALGEBRA I BIM.

TRILCE PRIMARIA

LOCUTORIO REN@TRIXCEL :992444616



ALGEBRA

Í n d i c e

Pág.

å Introducc!n"""""""""""""""""""""""""""""""""""""""""""""""""""""##

å O$%r&con%' co()n&d&' %n N"""""""""""""""""""""""""*1

å O$%r&con%' co()n&d&' %n +""""""""""""""""""""""""*,

å Pot%nc&c!n I"""""""""""""""""""""""""""""""""""""""""""""""""""*#

å Pot%nc&c!n II""""""""""""""""""""""""""""""""""""""""""""""""""9-

å R&dc&c!n I"""""""""""""""""""""""""""""""""""""""""""""""""""""9,

å R&dc&c!n II""""""""""""""""""""""""""""""""""""""""""""""""""""99

å O$%r&con%' co()n&d&' con $ot%nc&c!n. r&dc&c!n""""""""""""""""""""""""""""""""""""1/1

COLEGIO TRILCE P0n& 2



ALGEBRA

¿Qué conoces acerca del origen de la palara !lgera"

E (&t%(0tco 0r&)% A)u&d&& Mo3&(%d I)n Mu'& (0' co(5n(%nt% &(&do

ALUARI7MI d%'$u8' d% %'tud&r %n & Ind& . &'(&r & c%nc& 3nd5 %'cr)%

'u &(o'o )ro AL ;ABR <=AL MU>ABALA ?u% ?u%r% d%cr Tr&n'$o'c!n .

R%ducc!n d% t8r(no' '%(%&nt%'" A $rnc$o %'t& nu%& d'c$n& '%

d%'n! con % no()r% co($%to d% & o)r& d% Au&r( $%ro .& %n % 'o

XI '% 'u$r(D& & '%und& $&rt% $&r& &(&r '($%(%nt% A d&)r o '%&

%)r& & & t%orD& d% &' %cu&con%'"

¿Quién #ue el principal #or$ador del !lgera %oderna"

PACCI&LI F144, 1,19H

E'tuo (u. &do & &rt% . & &

t8cnc& r%n&c%nt't& t&&n& %n 1494

$u)c& 'u (onu(%nt& o)r& Ju((& d%

Art(8tc& %)r& . G%o(%trD& %n &

cu& u%c& cud&do'& . d%t&&d&(%nt%

todo % conoc(%nto (&t%(0tco 3&'t&

%ntonc%'

d%'&rro&do . cu.& r0$d& du'!n

u% % nco d% un nu%o

Kor%c(%nto d% %)r&"

P&cco t&()8n '% &d%&nt! con %'t& o)r& & d&r un& '!n d% o'$ror%'o' ?u% %n o' 'o' $o't%ror%' '% %&rD&n & 3&c%r"

COLEGIO TRILCE P0n& -



ALGEBRA

SIMBOLOGÍA ALGEBRAICA

S Í M B O L O S I G N I F I C A D O

× • ( ); ;

( ) ; [ ] ; { }

M ( x ; y ) = 2 x y 2

P ( x ) = x + 2 x + 12

x

O p e r a d o r e s d e l a m u l t i p l i c a c i ó !

O p e r a d o r e s d e l a d i " i s i ó !

O p e r a d o r r a d i c a l !

# i $ o s d e a $ r u p a c i ó % p a r & t e s i s ' c o r c e t e s yl l a " e s ' r e s p e c t i " a m e t e !

M o o m i o d e " a r i a l e s * x * e * y * !

P o l i o m i o d e " a r i a l e * x * !

a r ia l e ' e s d e c i r l e t r a , u e p u e d e t o m a r " a r i o s" a l o r e s !

P a r a t o d o !

- i . e r e t e !




ALGEBRA

E'ERCICI&(

Ut&ndo o' o$%r&dor%' d% (ut$c&c!n . d'!n %%ctu&r:

L& (ut$c&c!n d% - $or * L& d'!n d% 14 %ntr% 2

'% %'cr)%: - * 24 '% %'cr)%: 14 ÷ 2 #

- " * 24 14 : 2 #

F- *H 24

Co($%t& '%5n o' %%($o' &nt%ror%':I" L& (ut$c&c!n d% , $or # A" L& d'!n d% -, %ntr% ,

'% %'cr)%: '% %'cr)%:

II" L& (ut$c&c!n d% 9 $or * B" L& d'!n d% 4* %ntr% 6

COLEGIO TRILCE P0n& ,



ALGEBRA

'% %'cr)%: '% %'cr)%:

III" L& (ut$c&c!n d% 6 $or 9 C" L& d'!n d% 6- %ntr% #

'% %'cr)%: '% %'cr)%:

Co($%t&r '%5n % %%($o:

MFQ.H -Q4.,4& PFQ.H #Q6.,

L&' &r&)%' 'on: Q . L&' &r&)%' 'on: Q .

E co%c%nt% %': -& E co%c%nt% %' : #

I" RF&)cH #&6)9c# II" +F(n$H 4(#n-$2

L&' &r&)%' 'on: L&' &r&)%' 'on:

E co%c%nt% %' : E co%c%nt% %' :

III" SFQ.H -1Q4.*& I" JFQ.H 2&)Q9.12

L&' &r&)%' 'on: L&' &r&)%' 'on:

E co%c%nt% %' : E co%c%nt% %' :

" PF.H #.# &.6 I" RFH )9 #, -

L&' &r&)%' 'on: L&' &r&)%' 'on:

Lo' co%c%nt%' 'on: Lo' co%c%nt%' 'on:




ALGEBRA

REGLA( )E &PERACI*+

Caso ,- (in signos de agrupacin

&" Pr(%ro '% r%'u%%n &' $ot%nc&' . r&Dc%' & & %"

)" J%undo '% r%'u%%n &' (ut$c&con%' . d'on%' & & %"c" Por 5t(o '% r%'u%%n &' &dcon%' . 'u'tr&ccon%' & & %"

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T 9

=+ - + 2"

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)" Lu%o '% $roc%d% co(o %n % c&'o &nt%ror Fc&'o 1H

[ (

3 º 2 º 1 º

) ]

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2 F H T , F H

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O O O O O G O O O O O

O O O O O G O O O O O N

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0A1&RA2 1A3L& T45

A" R%'o%r:

COLEGIO TRILCE P0n& #



ALGEBRA

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4" E tr$% d% doc% d'(nudo %n % du$o d% nu%%"

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'ERARQ6ÍA 7 (ÍMB&L&( )E C&LECCI*+

&ser8acin-

R%cu%rd& r%'o%r $r(%ro &?u%&' o$%r&con%' co()n&d&' ?u% '% %ncu%ntr&n (0'& nt%ror d% o' 'no' d% co%cc!n"

COLEGIO TRILCE P0n& *

R % c u % r d & r % ' o A % r d %

B ? u % r d & & d % r % c 3 & "



ALGEBRA

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,

0A1&RA2 1A3L& T45

R%'o%r &' 'u%nt%' o$%r&con%' co()n&d&'"

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3" 6/ F4 2H ,V R$t&" 61




ALGEBRA

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COLEGIO TRILCE P0n& 1/



ALGEBRA

E%($o -: R%'o%r E%($o 4: R%'o%r

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ALGEBRA

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E r%'ut&do: &( '% d%no(n& $ot%nc&

;% dond%:




ALGEBRA

=

=

on%nt%%Q$(

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c" ,2 , " , 2, " 2, 2 " 2 " 2 " 2 " 2 -2

AH EQ$r%'& o 'u%nt%:

J%' %%&do & cu&dr&do :

Oc3o %%&do & cu&dr&do : Q %%&do & cu&dr&do :

Cu&tro %%&do & cu)o :

Cnco %%&do & cu)o :

Nu%% %%&do & cu)o :

Tr%' %%&do & & cnco :

Cnco %%&do & & '%' : Q %%&do & & cu&tro :

E;P&+E+TE +6L& F;%nc!nH:

a : ,< I & /

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#

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=

2 - N 2/

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1H22F /= F1//1H/ 1

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R % c u % r d & :

L & ' ' u % n t % ' $ o t % n c & ' ' o n & ' ( 0 ' u t B & d & '

% n % c u r ' o " P o r o ? u % r % c ) % n % n o ( ) r %

d % n o t & ) % ' "

COLEGIO TRILCE P0n& 1-



ALGEBRA

2/ 21 22 2- 24

2, 26 2# 2* 29

21/ -/ -1 -2 --

-4 -, 4/ 41 42

4- 44 ,/ ,1 ,2

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6- #/ #1 #2 #-

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91 92 9- 1// 1/1

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142 1,2 162 1#2 1*2

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,. Produc=o de po=encias de igual ase-




ALGEBRA

a . a : a% n % > n R % ' u t & & ( ' ( & ) & ' % . % % Q $ o n % n t %

n & % ' & d % o ' % Q $ o n % n t % '

n c & % ' "

s u % a

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a

a

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n R % ' u t & & ( ' ( & ) & ' % . % % Q $ o n % n t %

n & % ' & d % o ' % Q $ o n % n t % '

n c & % ' "

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PARTE PR!CTICA

1" EQ$r%'&r co(o $ot%nc& c&d& c&'o:

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COLEGIO TRILCE P0n& 1,



ALGEBRA

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)" B F1-H- F1-H6 F1-H/

c" C F-H/ F-H1 F-H2 F-H- " " " " " F-H1/

4" R%ducr c&d& c&'o:

&" 1,#

9/,/2/

4

4"4"4X =




ALGEBRA

)" 16*

*6424

2"2

2"2"2"2"2 _ =

c" 61/

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? a @ : a . n n n

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)" 6- " #- Y6F#HZ- 42-

c" Q, " ., FQ.H,

/. Resolucin de ecuaciones eponenciales-

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⇒ -Q -4 2 ,⇒

1,,

1/1/Q

,

,2

=

⇒ -Q -11 ∴ Q 11 ⇒ 2/

2/Q

,

,2 =

⇒ 2Q ,/ ⇒ 2Q 1 ∴ Q /c" Indc&r % &or d% Q %n:

,1- -- " 1#Q

COLEGIO TRILCE P0n& 1#

J & ' ) & ' % ' ' o n u & % '

o ' % Q $ o n % n t % ' t & ( ) 8 n

' o n u & % ' "



ALGEBRA

⇒ F- " 1#H- -- " 1#Q

⇒ -- " 1#- -- " 1#Q ∴ Q -

PARTE PR!CTICA

1" ^&&r Q %n c&d& c&'o:

&" 1/

2-,Q

4

4"4"4* =

)" 9

1/-2

2

2"2"2Q =

c" F24H2 F12H2"2Q

d" ,

4-21/Q

,

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%" *Q 4-

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COLEGIO TRILCE P0n& 1*



ALGEBRA

√ * 1 N -4

r & D B

r & d c & n d o

D n d c %

o $ % r & d o r ( & t % ( 0 t c or & d c &

L& r&D cu&rt& d% *1 %' - .& ?u%: -4 *1"

E%($o':

,12,-

= → ,- 12,

-2#-

= → d%)do & ?u%: -- 2#

2164 =→ d%)do & ?u%: 24 16

2-2,

=→ d%)do & ?u%: 2, -2

21/241/

=→ d%)do & ?u%: 21/ 1/24

14196 = → d%)do & ?u%: 142 196

L & r & d c & c ! n % ' & o $ % r & c ! n n A % r ' && & $ o t % n c & c ! n "

J %n % Dndc% d% o$%r&dor r&dc& no &$&r%c% nn5n n5(%ro '% 'o)r%%nt%nd% ?u% %' % do' F2H" E' d%cr: r&D cu&dr&d&"

9→ r&D cu&dr&d& d% 9

-,12

→ r&D c5)c& d% ,12 ,-12, → r&D ?unt& d% -12,

PR&PIE)A)E(1" R&D d% un $roducto: 2" R&D d% un coc%nt%:

n n n nB

An

B

A=

6-"2

2#"*H2#HF*F ---

=

=

=

2

2

4

16

2,6

16

2,64

44

=

=




ALGEBRA

0A1&RA2 1A3L& T45A" ^&&r c&d& un& d% &' r&Dc%':

B" En tu cu&d%rno r%duc% &d%cu&d&(%nt% c&d& %Q$r%'!n:

COLEGIO TRILCE P0n& 2/



ALGEBRA

Eponen=e #raccionario-

%

n : %n I ( n I n 2+

4 -4

-

QQ =

2*** -- 1-

1

=

4161621

=

9--- 2,/

1//,/ 1//

=




ALGEBRA

444 2/2/

2/ 2/= ⇒

nnQ N Q ⇔ Q ` /

0A1&RA2 1A3L& T45

A" R%$r%'%nt& c&d& r&D u'&ndo %Q$on%nt% r&ccon&ro:

&" =

- ,4

)" =#2

c" =

4 -Q

B" R%$r%'%nt& c&d& %Q$r%'!n (%d&nt% r&dc&%':

&" =

#1

2

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,

2

-

c" =11

2

Q

C" Con'd%r&ndo & d%nc!n d% %Q$on%nt% r&ccon&ro . o %'tud&do %nR&dc&c!n I d%'&rro& %n tu cu&d%rno o' 'u%nt%' %%rcco':

1" 169196

-61//A

=

2" -

-62-66B ++=

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,/ 1//4/ 12/-/ 6/ 4-2; ++=

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−

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--

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46

4#

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6

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ALGEBRA

1" J: 6

1

,

1B.

,

4

-

1

2

1A

ndc&r % &or d% Q ': B

AQ =

2" J:-- ,12.#29Q ==

ndc&r % &or d%:/22 HQ.F.QE

E" ^&&r Q %n:

14*

6-9,Q

2"*

2"*"2"*64 =

P&TE+CIACI*+ 7 RA)ICACI*+P&r& $od%r r%&&r %n or(& corr%ct& o' %%rcco' d% %'t% c&$Dtuo d%)%(o' t%n%r(u. %n cu%nt& &' r%&' d% &' o$%r&con%' co()n&d&'" R%cord&ndo ?u% &$ot%nc&c!n %' un& (ut$c&c!n . & r&dc&c!n %' 'u o$%r&c!n n%r'& $or o t&nto$o'%%n & ('(& %r&r?uD&"

^&. ?u% r%'$%t&r &' 'u%nt%' r%&':1[ J% d%'&rro&n &' (ut$c&con%' d'on%' r&dc&%' . $ot%nc&' ' %'to' 'on

dr%cto' $&r& 'u &$c&c!n"2[ R%cu%rd& o' r&dc&%' '% &$c&n 'o)r% un n5(%ro" Por o ?u% $r(%ro 3&. ?u%

r%ducr % r&dc&ndo"-[ Lu%o '% r%duc%n &' 'u(&' . r%'t&' r%'$%t&ndo o' 'no'"4[ J %Q't%'%n $&r8nt%'' .ao corc3%t%' '% r%duc%n d%'d% o' (0' nt%rno' 3&c& o'

(0' %Qt%rno'",[ J no %Q't%'%n 'no' d% &ru$&c!n '% d%'&rro& d% ?u%rd& & d%r%c3&"

E%($o:

⇒

2##

,-

24214*1

121-E

÷

=

44#9

112#E

,

=

*1*1616

E ,,

=

-9*1E =

COLEGIO TRILCE P0n& 2-



ALGEBRA

Algebra i Bim

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