Taller Matematicas
September 6, 2022 | Author: Anonymous | Category: N/A
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SH@E@HSVL
ENVCENV@KN CEWRC[NR@NO.
COY@ NRRCMS@
272>
Sh`fnf > Nkt`v`fnf 2 Vnoocr pnrtc 2: Wltchk`nk`ûh y rnf`knk`ûh
>. St`o`k St`o`kc c ons prl prlp`c p`cfnf fnfcs cs fc on plt pltchk chk`nk `nk`ûh `ûh y on rnf rnf`kn `knk`û k`ûh h pnr pnrn n s`epo` s`epo`i`k i`knr nr knf knfn n cjcrk`k`l: n. (2 )−3 23 2
6
0
;
b. ( 0 ) ý ( 6 ) 3 3 k. √ 4 √ 6 [louk`ûh: n. ( 2 )−3 23 2−3 +3
2
7
5 >
2
b .(
6 0
6
;
0 6
) ý( )
2
6
;
( ) ý( ) 0
6
0
2+ ;
( ) 5 0
3 3 k . √ 4 √ 6 5
6
3
( ) 5 0
4 √ 6
6 0
5 4.2 5>9
2. Dnooc co vnolr h, fc ilren quc ons prlpls`k`lhcs scnh k`crtns:
h n. √ √ √ 256 ; √ 2 52 h b.
4
h ; k. ; √ ; √ ; 5;
[louk`ûh: h n. √ √ √ 256
2
> 6
√ 2
5 6 h
;
b.
4
52 h 5 2
2
−4 ;
> 6
5 22 h
5 2h
h5
k.
;
−4 ;
; √ ; √ ; ;
>> 9
5;h
¼ ;h 5
>> 9
5h
h5
>> 9
> 6
5 2h
h5
> 4
;. [`epo`i`quc: n. 6 √ >>2 >>2 − √ >=3 >=3 + √ 9; 9; b. √ >>2− √ 9; 9; + √ >=3 >=3 + √ >94 >94 37
27
+ −2 √ 27í >23 √ 3 √ >23
k. [louk`ûh:
n. 6 √ >>2 >>2 − √ >=3 >=3 + √ 9; 9; 5
6
√ 2
6
.=
¼ 6 ( 2 ) √ = −3 √ = + ; √ = 2
¼ >9 √ =−3 √ = + ; √ =5>6 √ =
f. √ >>2− √ 9; + √ >=3 + √ >94 5 √ =− ¼+√ 23 23 + √ 26) √ = ( 6 - ; + 3 + 2 √ 9 )
√ = ( 9 + 2 √ 9 )
√ = √ 9 (√ 9 + 2 ¼
5 √ 62 62 ( √ 9 + 2 )
k.
37
+
27
>23 √ 3 √ >23
−2 √ 27
37 3 √ 3
5
+ 6 √ 3 - 6 √ 3 5
>7
√ 3
52 √ 3
>7
√ 3
+6 √ 3 - 6 √ 3
−√ 3 .= +√ ; 2
2
.=
6. Fcsnrrlooc y s`epo`i`quc: −;
2
n. ( 4> ) 6 + ( 2>9 ); −2
2
;
;
b. ( 2= ) + ( 96 ) −2 ; k. ( 96 ) 3 + ( 923 ) 6 [louk`ûh: −;
2
n. ( 4> ) 6 + ( 2>9 ); −; ;
+( 9 ) 2 ;
; >
2
+( 9 ¼ ¼ ; ) ¼ 5
;
;
;
>
> 2
5 2= +9 5¼ 2= +
−2
2
;
;
b. ( 2= ) + ( 96 ) >
5 2= 2
5¼
¼
;
5 5
2 ;
>
¼¼ >
¼¼
5
>
¼¼
5
−2
+
> >66 0
>63
5
0
;
K. ( 96 ) 3 + ( 923 ) 6
> 2 96 3
6
;
>
6
96 √ 96
+ (3 ¼ 5
3
96 √ 96 +3 5 +>23 3
;
;
2
96
> ;
;
2
+ 9
+
;9 >
> 0=2
5
2=
0=;
5
2=
3. On iuhk`ûh fc Klbb-Flumons, quc cs cepocnfn ch cklhleån, eucstrn on rconk`ûh fc ols `hsuels y co h`vco fc prlfukk`ûh. F`kdn iuhk`ûh iuc prcschtnfn plr Kdnrocs Klbb y Wn Wnuo uo Fl Flum umon ons, s, ch >0 >024. 24. Cs Cstl tlss fl flss cklh cklhle le`s `stn tnss co conb nblr lrnr nrlh lh uh el elfc fcol ol fc fcoo krck`e krc k`e`ch `chtl tl fc on ckl cklhle hleån ån cst cstnfl nfluh`f uh`fchs chsc c fur furnht nhtc c co pcr pcr`lf `lfl l >400 >400->02 ->022. 2. Nså Nså,, busknrlh prcschtnr uhn `fcn s`epo`i`knfn fc cklhleån, ch co quc on prlfukk`ûh fcpchfc, pr`hk`pnoechtc, fc fls inktlrcs: trnbnjl y knp`tno. Cstc elfcol rcsuotû bnstnhtc prck`sl. On iuhk`ûh fc Klbb-Flumons sc cxprcsn fc on s`mu`chtc ilren: ξ
β
P 5 N O A
Flhfc P5 Wrlfukk`ûh tltno (vnolr elhctnr`l elhctnr`l fc tlfls ols nrtåkuols nrtåkuols prlfuk`fls ch uh nþl) O5 Vrnbnjl (húecrl tltno fc pcrslhns/dlrns trnbnjnfns ch uh nþl) A5 Knp`tno (vnolr elhctnr`l fc tlfn on enqu`hnr`n, co cqu`pne`chtl y ols `heucbocs) N5 Inktlr fc prlfukt`v`fnf prlfukt`v`fnf ξ y β slh slh ons ons co cons nst` t`k` k`fn fnfc fcss fc ol olss inkt inktlr lrcs cs fc pr prlf lfuk ukk` k`ûh ûh,, tr trnb nbnj njl l y kn knp` p`tn tno, o, rcspckt`vnechtc. rcspckt`vnecht c. [lh vnolrcs klhstnhtcs fctcre`hnfls plr on tckhlolmån. Fctcre`hc P npo`knhfl ons prlp`cfnfcs fc on pltchk`nk`ûh: e e ;e
n. N 52 1 O 5
2
;
1 A 5
;e
4
2
3
e
>7
>
>
2
2
1 ξ 5 1 β 5
3
>
−2
3
3
− − b. N 52 1 O52 x y 1 A 5 6 x y 1 ξ 5 1 β 5 2
2
2 ; k. N 5n 1 O5
f. N 5 [louk`ûh:
√ ;
>
2
−;
>
1 A 5n
>
6
¼
>2 3
(n )
−;
6
4n
;
;
2= b
1 O5
n
0
−>
b
2
1 A 5
b
6 2
n0
1 ξ 5−> 1 β 5−>
;e
e
>
3
2
>7
y 5 2 . ¼) . (
e)
> 2
>
2; e. ¼) .¼ )> / ¼2 ¼ 2
>
;e
. ¼) . 2−> / ¼2 ¼ 2
;e
. ¼) . 2−> / ¼2 ¼ 5 2; e. 2
2
2
−; / 6 >
>
2
2
3 /2
−>
2
2
. 2−> / ¼ ¼ 5
0 / 6 e
2
2
k. P5 2 (2 x y ¼ > / 3 ( 6 x y ) P5 23 /2 . 2> /2 . x 2 /3 . y > /3 . 6 2/3 . x−2/ 3 . y 6 /3 6 2 /3
52 / . 2 / . x 3 2
> 2
/
2 3
.y
/
> 3
.2
/
−2 / 3
6 3
.x
.y
/
6 3
/
= 2
2
.y
5√ 2 y 52; √ 2 y 5 4 √ 2 y =
f. P5 n 2/; ( 5 n 2/; . (
>
−;
−>
¼ > / ¼2 ¼ (n 6 ( n2 ) >9 (n ¼¼ > /2 ¼ ¼ 3 ¼ ) > / ¼ ¼ ¼ ¼ 2
> 3 / >2
n
2
¼ > / ¼ . ¼(n− / . n− / ¼ > / ¼ ¼ ; 6
2
> 4
−=
5 n 2/; . n−3 / 26 . ( n 4 ) > / ¼2 ¼ 5 n 2/; . n−3 / 26 . n− / 5 n = 9
√
c. P5
;
;
4n
;
2= b
.
5√ 4 √ n . ;
;
;
/¼
b
n
/
6 0
;
>
n
.
2 /0
−; / 6 5
b
;
−> /2
/
2 0
n
b n 5 b . 6/ 0 . −; / 6 n b ; 2
64
¼− − ¼ ¼ . ( ¼
−> /2
b
5 √ n
0
6 (n −> /2
2= √ b √ 2= ;
/
> 64
b− ; / 6 /
2 0
n
>
¼ −¼ ¼
-
> 2
n 3/ 0
5
2
b
;
. b 6 . n2/ 0
n 3 /0
5
2
b ; /6
;
2 /0
. . n 5
2n
=/0
b;/6
;
5 2 √ n / ; √ b; 0
=
6
9. Co `htcràs klepucstl cs nquco `htcràs quc sc klbrn l sc pnmn plr uh kràf`tl l uh ndlrrl. Kunhfl sc o`qu`fn sc nkueuon no knp`tno (knp`tno`znk`ûh fco `htcràs). Chtlhkcs, ch on s`mu`chtc o`qu`fnk`ûh fc `htcrcscs, co `htcràs nhtcr`lr ilren pnrtc fco knp`tno l bnsc fco kîokuol fco hucvl `htcràs. Co vnolr nkueuonfl klh co `htcràs klepucstl sc knokuon fc on s`mu`chtc enhcrn: h
Y 5 W ( >+ ` )
Flhfc W5 Knht`fnf prcstnfn `5 Vnsn fc `htcràs tr`ecstrno h5 Huecrl fc tr`ecstrcs quc furc co pràstnel. n. Eûh`kn fcpls`tû $>.277.777 ch uhn cht`fnf i`hnhk`crn quc rcklhlkc `htcrcscs fco >2 % nhuno, knp`tno`znboc tr`ecstrnoechtc. ¼Kuîhtl tchfrî nkueuonfl ch on kuchtn no i`hno`znr co tcrkcr nþl< ¼Kuîo cs co `htcràs mchcrnfl ch co pr`ecr tr`ecstrc< b. @munoechtc, ¼kuîo cs co `htcràs mchcrnfl ch co scmuhfl, tcrkcrl y kunrtl tr`ecstrcs< [louk`ûh:
.
Y5 W (>+` ¼ ¼ h >.277 7 .777 ¼ Y5 >.27
b. Y5
>.277 >.27 7 .777
¼
¼ >277.777 (>90) 5 272477777 >.277 7 .777 ¼5 >277.777 ¼ Y5 >.27 ¼ >277.777 (2>0=) 5 29;9677777 >.277 7 .777 ¼5>277.777 ¼ Y5 >.27 ¼ >277.7775( 2439> ) 5;62=;2
=. On tnsn cickt`vn nhuno klhst`tuyc co kr`tcr`l pnrn tlenr fck`s`lhcs, `hvcrt`r oûm`knechtc y csklmcr nqucoon cht`fnf quc lirczkn on tnsn eîs notn (s`h klhs`fcrnk`lhcs plr ndlrn fco r`csml), y, pnrn chfcufnrsc, chfcufnrsc, cocm`r nqucoon tnsn quc, ch tàre`hls cickt`vls, scn on echlr. [` on tnsn cickt`vn nhuno (V.C.N) cstî fnfn plr V . C . N 5Q( > +
` )¼ ¼ e −> U>77 ¼ e
Flhfc `5 @htcràs hle`hno e5 Wcr`lfl fc knp`tno`znk`ûh no nþl Conblrc uhn tnbon ch on quc `oustrc on cvlouk`ûh fc uhn kuchtn fc ndlrrl quc t`chc uh rchf`e`chtl fco >6 % ecs vchk`fl, s` ch on kuchtn sc fcpls`tnh $3.777.777 quc pcrenhckch furnhtc 9 ecscs ch co bnhkl n. Klh `htcrcsc s`epocs b. Klh `htcrcsc klepucstl
@HVCRC[C[ [@EWOC[
EC[C[
[NOFL
@HVCRC[ FCO WCR@LFL
KNW@VNO I@HNO
@HVCRC[C[ NKSESONFL[
@H@K@NO > 2 ; 6 3 9
$ 3.777.777 $ 3.777.777 $
$ =77.777 $ =77.777 $
$ 3.777.777 $ 3.777.777 $
3.777.777 $ 3.777.777 $ 3.777.777 $ 3.777.777
=77.777 $ =77.777 $ =77.777 $ =77.777 $ 6.277.777
3.777.777 $ 3.777.777 $ 3.777.777 $ 3.777.777 $ 0.277.777
KNW@V KNW@VNO NO @H@K @H@K@NO @NO WONZL
$
$ =77.777 $
>.677.777
$
2.>77.777
$
2.477.777
$
;.377.777
$
6.277.777
3.77 3.777. 7.77 777 7
9 >6%
@HVCRC[
@HVCRC[C[ KLEWSC[VL[
EC[C [ > 2 ; 6 3 9
[NOFL @H@K@NO
$ 3.777.777 $ 3.=77.777 $ 9.604.777 $ =.67=.=27 $ 4.666.47> $ 0.92=.7=;
@HVCRC[ FCO WCR@LFL
KNW@VNO I@HNO
@HVCRC[C[ NKSESONFL[
$ =77.777 $ =04.777 $ 070.=27 $ >.7;=.74> $ >.>42.2=2 $ >.;6=.=07 $ 3.0=6.49;
$ 3.=77.777 $ 9.604.777 $ =.67=.=27 $ 4.666.47> $ 0.92=.7=; $ >7.0=6.49; $ >7.0=6.49;
$ =77.777 $ >.604.777 $ 2.67=.=27 $ ;.666.47> $ 6.92=.7=; $ 3.0=6.49;
4. Sh ko`cht ko`chtc c fck` fck`fc fc `hvcr `hvcrrr $273 $273.7 .777 77 no 24 % nh nhun unoo kl klep epuc ucst stl l kl klh h pnml pnml fc `h `htcr tcrcs cscs cs f`nr`l f`nr`ls. s. n. Fctcre`hc on tnsn cickvn nhuno, s` on knp`tno`znk`ûh cs b`ecstrno. @HVCRC[ V@CEWL L WCR@LFL
7,24 9
VCN
;>,6==>=;4
`/e
7,7699999= On knp`tno`znk`lh b`ecstruno cs fc ;>,6=%
b. Fctcre`¬hc on tnsn cickvn nhuno, s` on knp`tno`znk`ûh cs tr`ecstrno.
@HVCRC[ V@CEWL L WCR@LFL
7,24 6
VCN
;>,7=097>
`/e
7,7= On knp`tno`znk`ûh cs fco ;>,7=%
Fctcre Fctc re`hc `hc kuîo kuîo cs on ec ecjl jlrr lp lpk` k`ûh ûh pn pnrn rn co ko`chtc. k.
On ecjlr lpk`ûh pnrn `hvcrr fcbcrî scr on tnsn fc `htcrcs eîs notn y mchcrc rchtnb`o`fnf, co ko`chtc fcbcrî csklmcr co ;>,6=% klh knp`tno`znk`ûh b`ecstruno
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