Resolucion de Problemas

 

Wâlkblms g` r`sdhulbük r`sdhulbük g`  g` prdnh`oms  prdnh`oms

 

  mm   s `   r  mm  hh   kk d s  m    p p  l d,   ââ l k b  ll m  b b l  t  í  ` o   `` s t  mm  tt    s t `  s  b    s s  `  g d  d    ll d k  `  ss  y   k   o o d g  k  k   o o â t d s b  s  s `    uu k  d   q  q  u  d n h  `` o m s  s, ,,  ss b b   kk d   mm k í h  bb  s  `  g  yy   s  h  l  m  ý m  uu  `  pp r  dd   n  m  ` ` `  g  `      r r  s  k  ` o   pp m r  mm   yy  dd f  mm k s b  ``   gg  d  n   n h `  \ `  ``  h  uu l b  üü k  s  pp r d  g d s  l b  dd k ` s  y m  hh  mm     d d    d d  t  d  h h  s  â   o  s  dd p  `` x l h  uu  r  ``  b k  m k  m k  o   k  o   ll b  dd k  s b  n h  ``   q   u `  q   ` h b b o  r  d  d   pp  u k g  p d  p r  dd   uu m l b  üü k  `` h  o   o  r  bb  dd  h  ` v m  k f  dd l m r  k ` l ` s m  g `  ``  t  rr  ââ s  bb  kk  s  ` h  ``

^`sdhulbük g` prdnh`oms

@h `stugbd g` hm r`sdhulbük g` prdnh`oms vbkd g` hm omkd ldk `xp`rbo`ktmh,, nmsíkgds` `k `h `stugbd g` hds hm psbldhdiïm `xp`rbo`ktmh  prdl`sds ldikbtbvds ldikbtbvds qu` sbiu` sbiu`kk hms p`rsdkms pmrm r`sdh r`sdhv`r v`r  prdnh`oms bkt`h`ltumh`s bkt`h`ltumh`s Fu`kt`s prbklbpmh`s ᴣ Lr`lb`kt` bkt`râs bkt`râs `k `h `stugbd g` hm

lr`mtbvbgmg ᴣ \uribob`ktd g`h `kfdqu` g` ldop`t`klbm sdlbmh `k hm  psbldpmtdhdiïm vs odg`hd prdf`sbdkmh prdf`sbdkmh

ᴣ G`smrrdhhd g` hm t`drïm ᴣ G`smrrdhhd g` `xpmksbük g`h

trmksmllbdkmh `strâs

`kfdqu` ldikbtbvd ldkgultumh

`k hm odgbfblmlbük g`  

Gezurbhhm y Idhgfrb`g (=210,  píi.=26) ldkgultm  kdromh‟ kdromh‟ d ‘ p`rturnmlbük   p`rturnmlbük `odlbdkmh‟ `odlbdkmh‟ pu`g` Irmk pmrt` g` hd qu` ldksb ldksbg`rmods g`rmods lhïkblmo`k lhïkblmo`kt` t` ldod ‘‘ldkgultm v`rs` ldod ldkgultm bk`fblmz y sus ldks`lu`klbms, g` r`sdhv`r g`t`robkmgds prdnh`oms sbtumlbdkmh`s, g` su vbgm y sus bkt`ktds bkmg`lumgds bkmg`lumgds pmrm r`sdhv`rhds tb`k` `f`ltds bkg`s`mnh bkg`s`mnh`s, `s, tmh`s ldod mksb`gmg g`pr`sbük y hm lr`mlbük g` prdnh`oms mgblbdkmh`s

 

Omadk`y y Mrjkdff (=291) gbstbkiu`k tr`s irupds g` tâlkblms ldikbtbvms `ktr` hms qu` s` bklhuy`k hms tâlkblms g` r`sdhulbük g` prdnh`oms, amnbhbgmg`s g` `kfr`ktmob`ktd y r`strulturmlbük ldikbtbvm tâlkblms g` r`sdhulbük g` prdnh`oms ‘Pk prdl`sd ldikbtbvd-mf`l ldikbtbvd-mf`ltbvdtbvdldopdrtmo`ktmh o`gbmkt` `h lumh uk bkgbvbgud d irupd bg`ktbfblm d g`slunr` o`gbds `f`ltbvds pmrm sdhulbdkmr ldkfhbltds prdpbds g`h qu` aml`r ldtbgbmkd‟ ^`sdhulbük g` ldkfbltds vbmh`s ᴣ Ldkfbltds sdlbmh`s ᴣ Urdnh`oms bkt`rp`rsdkmh`s ᴣ Urdnh`oms p`rsdkmh`s ᴣ Urdnh`oms mphblmgds

Fbkmhbgmg t`rmpâutblm3 Wrmtmob`k Wrmtmob`ktd td g` prdnh`oms  psbldhüiblds  psbldhüibl ds qu` sdk r`suhtm r`suhtmgd gd g` gâfblbt `k amnbhbgmg`ss pmrm r`sdhv`r ldkfhbltds p`rsdkmh`s amnbhbgmg` \ïktdoms

Fbkmhbgmg pr`v`ktbvm3 @ktr`kmob`ktd `k r`sdhulbük g`  prdnh`oms pmrm o`cdrmr o`cdrmr hms amnbhbgmg`s pmrm pmrm aml`r fr`kt` m hms pdt`klbmh`s sbtumlbdk`s ldtbgbmkms  prdnh`oítblms

 

Nms`s t`ürblms y `xp`rbo`ktmh `xp`rbo`ktmh`s `s @xp`rbo`ktmlbük `k r`sdhulbük g` prdnh`oms

Mphblmlbdk`s ldk mkbomh`s Bkv`stbimgdr`s ldod Jdah`r Bkv`stbimgdr`s Jdah`r,, `xmobkmrdk s`lu`klbms g` r`spu`stms `k labopmklâs qu` ldkgulïmk m hm sdhulbük g` g`t`robkmgds prdnh`oms r`hmlbdkmgdss ldk hm dnt`klbük g` mhbo`ktds, tmh`s ldod ldhimr ukds r`hmlbdkmgd  phítmkds g`h t`lad t`lad fu`rm g`h mhlmkl` gg`h `h mkbomh Ldklhusbdk`s ]u` mhid sul`g` `ktr` `h `stbouhd y hm r`spu`stm qu`gmkgd lhmrd qu` `xbst`k  prdl`sds o`gbmlbdkmh`s o`gbmlbdkmh`s `k prbomt`s y `k mkbomh`s fbhdi`kâtblmo`k fbhdi`kâtblmo`kt` t` bkf`rbdr`s

]u` `stds prdl`sds pu`g`k s`r `k dlmsbdk`s ldoph`cds, tmh ldod ldks`iubr qu` uk mkbomh mpr`kgm, o`gbmkt` mpr`kgbzmc` vblmrbd, ukm ldkgultm ldklr`tm.

 

@k Auomkds `k ldkgblbdk`s g` hmndrmtdrbd,

Lumh`s sdk hms amnbhbgmg`s ldkl`ptumh`s y hds prdl`sds ldikbtbvds bkt`rvbkb`kt`s `k hm r`sdhulbük g` prdnh`oms

Ldklhusbdk`s,

ᴣ @h s`r auomkd `s

`xtr`omgmo`kt` ldoph`cd, usmsbouhtmk`ms lmpmlbgmg`s  pmrm r`mhbzmr r`mhbzmr mltbvbgmg`s gbv`rsbfblmgms ᴣ Hm sdhulbük g` prdnh`oms r`qub`r` prdl`sds s`lu`klbmh`s

 

@k `h íonbtd bkgustrbmh ,

`h bkt`râs s` am gbrbibgd mh `ktr`kmob`ktd lr`mtbvd y `h g`smrrdhhd g` amnbhbgmg`s g` omk`cd g` sbtumlbdk`s

@strmt`ibms,

  ᴣ Wdrn`hhbkd g` bg`ms ᴣ \bk`tblm ᴣ Hm nbükblm

 

Íonbtd `sldhmr 

Íonbtd lhïkbld

ᴣ Urdirmoms pr`v`ktbvds ᴣ Urdirmom g` `ktr`kmob`ktd g` r`sdhulbük g`

@s ldoók qu` hm tâlkblm qu` r`sdhulbük g` prdnh`oms s` uhbl` `k hm prmllm lhblm `k ldkcuktd ldk dtrms tâlkblms pmrm trmtmr m hds pmlb`kt`s, ldk `h

 prdnh`oms `k tmr`ms bkstruo`ktmh`s bkstruo`ktmh`s ᴣ @ktr`kmob`ktd `k sdhulbük g` prdnh`oms pmrm

o`cdrmr `h lhbom sdlbmh `k `h muhm ` bkt`rv`kbr `k hds trmstdrkds g` hm ldkgultm

k g` o`cdrmr su lmhbgmg g` vbgm g`sg` hds gb`r`kt`s msp`ltds qu` pu`g`k mqu`cmrh`

 

Wâlkblm g` r`sdhulbük g` prdnh`oms prdnh`oms g` G·zurbhhm G·zurbhhm y Idhgfrb`g

 

Fms`s

Dnc`tbvds

@c`ophds

Drb`ktmlbük g`h prdnh`om

G`smrrdhhmr ukm mltbtug fmlbhbtmgdrm `k `h suc`td m hm adrm g` `kfr`ktmr `h prdnh`om

´]u` mltbtug a` g` t`k`r mkt` hds  prdnh`oms4 ᴣ \dy lmpmz g` r`sdhv`rhds `fblmzo`kt` ᴣ W`kid qu` r`ldkdl`rhds y kd `vbtmrhds ᴣ  Kd o` vdy m pr`lbpbtmr pr`lbpbtmr mh gmr ukm r`spu`stm

Fdro Fd rouh uhml mlbü bükk y g`fb g`fbkb kblb lbük ük g`h g`h prd prdnh nh`o `omm

G`fb G` fbkb kbrr `h prd prdnh nh`o `omm dp`r dp`rmt mtbv bvmo mo`k `kt` t` y  phmk`mr o`tms r`mhbstms r`mhbstms

´Lumh `s `h prdnh`om4 ᴣ Gbslutd oulad ldk ob pmr`cm ᴣ ]ubsb`rm pmsmrhm nb`k ldk `hhm y gbsfrutmr ldkcuktmo`kt` `h tb`opd hbnr`

I`k`rmlbük g` mht`rkmtbvms

Urdpdk`r ukm mophbm vmrb`gmg g` sdhulbdk`s pmrm muo`ktmr hm pdsbnbhbgmg g` sdhulbdkmr `h prdnh`om

´]u` pu`g` aml`r pmrm sdhulbdkmrhd sdhulbdkmrhds4 s4 ᴣ Umsmr oms tb`opd cuktds kd mhzmr hm vdz ᴣ Uhmk`mr smhbgms g` fbk g` s`omkm

 

Fms`s

Dnc`tbvds

@c`ophds

Wdom g` g`lbsbdk`s

Vmhdrmr hms ldks`lu`klbms g` lmgm mht`rkmtbvm y s`h`llbdkmr hms qu` pu`g`k

´]uâ ldks`lu`klbms k`imtbvms y pdsbtbvms o` pu`g` trm`r lmgm mht`rkmtbvm4

o`cdrmr ukm sbtumlbük

@c`lul @c` lulbdk bdk y v`rbf v`rbfblm blmlbü lbükk g` r`s r`suht uhtmgd mgdss

ᴣ Umsmr oms tb`opd cuktds ᴣ  Kd irbtmr  ᴣ Uhmk`mr mltbvbgmg`s g` dlbd

Udk`r Udk `r `k `k prmlt prmltblm blm hms g` g`sbl sblbdk bdk`s `s tdom tdomgms gms

Hh`vd m lmnd `stms mht`rkmtbvms y v`d sb

y ldoprdnmr hds r`suhtmgds

sdhulbdkmkr`vbsmr r`mho`kt` `h prdnh`m,. \b kd, `h prdl`sd

 

Wâlkblm g` sdhulbük g` prdnh`oms bkt`rp`rsdkmh`s bkt`rp`rsdkmh `s g` \pbvmlj y \aur` Dnc`tbvd `s muo`ktmr `h mcust` sdlbmh y hm ldop`t`klbm bkt`rp`rsdkmh bklr`o`ktmkgd hms amnbhbgmg`s bkt`rp`rsdkmh`s g` sdhulbük g` prdnh`oms. Hms amnbhbgmg`s qu` g` mlu`rgd ldk `stds mutdr`s obg`k `h mcust` sdlbmh y qu` bkt`ktmrmk g`smrrdhhmr sdk hms sbiub`kt`s3 ᴣ I`k`rmr sbtumlbdk`s mht`rkmtbvms m hds prdnh`oms ᴣ

bkt`rp`rsdkmh`s bkt`rp`rsdkmh `s (p`ksmob`ktd mht`rkmtbvd)

Amnbhbgmg hms pmrmo`tms g`t`robkmr hds o`gbds mg`lumgds pmrm ldks`iubr ᴣ \mn`r vmhdrmr hms ldks`lu`klbms g` lmgm ukm g` hms mht`rkmtbvms (p`ksmob`ktd ldks`lu`klbmh) ldks`lu`klbmh)

 

\dhulbük g` prdnh`oms `k kbýds pr``sldhmr`s @st` prdirmom ldkstm g` < fms`s   Fms` = Ldk `h dnc`td g` qu` `h kbýd qu` mgqub`rm lb`rtd gdobkd `k `h h`kiumc`

Fms` < Udr o`gbds g` gbnucds y ouý`lds qu` r`pr`s`ktmk sbtumlbdk`s bkt`rp`rsdkmh`s bkt`rp`rsdkmh`s y qu`  pb`ks`k `k hms pdsbnh`s pdsbnh`s sbtumlbd sbtumlbdk`s k`s

 

\dhulbük g` prdnh`oms `k kbýds `sldhmrbzmgds Wrmnmcmkgd ldk kbýds g` qubktds`lursd `kldktrmrdk hm amnbhbgmg g` p`ksmob`ktd o`gbds-fbk`s, h` pr`s`ktmnmk gbv`rsms abstdrbm ldk prdnh`oms g` hm vbgm r`mh y s` h`s p`gïm qu` `hhds ldoph`tmrmk hm abstdrbm.

Mrod qu` `h p`ksmob`ktd o`gbds-k`s p`robt` gb`r`klbmr kbv`h`s g` mgmptmlbük `ktr` irupds g` mguhtds y qu` `h p`ksmob`ktd ldks`lu`klbmh, gbskiu` m hds mgdh`sl`kt`s r`f`xbvds g` hds bopuhsbvds.

\dhulbük g` prdnh`oms ldk mgdh`sl`kt`s y mguhtds

 

Hm sdhulbük g` prdnh`oms bkt`rp`rsdkmh`s `k pmlb`kt`s  psbqubítrblds

@kldktrmrdk qu` hms amnbhbgmg`s g` p`ksmob`ktd o`gbds-fbk`s `rmk gbf`r`kt`s `k suc`tds sbk prdnh`oms sbikbfblmtbvds y `k suc`tds

 psbqubítrblds `rm g`gulb`kgd qu` `h mmcust` sdlbmh g`amnbhbgmg`s hds pmlb`kt`s hds o`kdr g`nbgd gâfblbt `k hms g` r`sdhulbük g` prdnh`oms bkt`rp`rsdkmh`s

 

Urdirmom g` \lb`kl` g` Omadk`y Ldksbst` `k `ktr`kmr mk suc`td g` tmh fdrom qu` s`m aínbh m hm adrm g` mkmhbzmr y g` lmonbmr su ldkgultm, qu` s`m uk lb`ktïfbld p`rsdkmh O`gbds pmrm fmlbhbtmr `h `ktr`kmob`ktd Odg`hmgd ᴣ^`fdrzmob`ktd sbst`oítbld ᴣ^`mhbzmlbdk irmgumh g` hms tmr`ms ᴣMqubsblbdk g` amnbhbgmg`s mutd `vmhumtbvms mgmptmtbvms

 

Hm lb`klbm p`rsdkmh `s uk prdirmom ldoph`td s`klbhhd y g` fílbh ldopr`ksbük sunrmym hm bopdrtmklbm g` lr`mr `k `h lhb`kt` hms amnbhbgmg`s g` `kfr`ktmob`ktd m hds  prdnh`oms pmrm qu` pu`gmk s`r oms `fblml`s

(\p`lbfbty) @sp`lbfblmr `h ír`m i`k`rmh g`h prdnh`om

(Ldhh`lt) ^`ldi`r bkfdromlbük

(Bg`ktbfy) bg`ktbfblmr hms lmusms

(@xmobkmt`) `xmobkmr hms sdhulbdk`s

(Kmrrdw) G`hbobtmr y `xp`rbo`ktmr 

(Ldopmr`) Ldoprmr `h prdir`sd

(@xt`kg) Mophbmr, r`vbsmr m r``ophmzmr hm sdhulbük

 

Lmrmlt`rïstblms ldouk`s y vmrbmkt`s g` hds prdirmoms Lmrmlt`rïstblms ldouk`s Fms` = G`fbkbr `h `str`sdr y r`mllbdk`s g` `strâs Fms` > `stmnh`l`r dnc`tbvds r`mhbstms Fms` < I`k`rmr ukm imom g` pdsbnh`s lursds g` mllbük mht`rkmtbvds Fms` 7 Bomibkmr y ldksbg`rmr ldod pdgrïmk r`spdkg`r dtrds suc`tds sb s` h`s  pbgb`rm qu` trmtmrmk y prdnh`om sbobhmr qu` i`k`rmrm `strâs •

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Fms` 0 @vmhumr hds prds y ldktrms g` lmgm mht`rkmtbvm mht `rkmtbvm

 

@tmpms ldouk`s `k hds `ktr`kmob`ktd `ktr`kmob`ktdss Ur`iuktms

@tmpms

´]u` o` pr`dlupm4

Bg`klmlbük g`h prdnh`om

´]u` qub`rd ldks`iubr4

\`h`llbük g` dnc`vds

´]u` pu`gd aml`r4

Nósqu`gm y `hmndrmlbük ` mht`rkmvms

´]u` pdgrïm dlurrbr4

Ldksbg`rmlbük g` hms ldks`lu`klbms

´]u` g`nd g`lbr4

Wdom g` g`lbsbdk`s

!Vdy m hh`vmrhd m hm prmllm!

Uu`stm `k prmllm

´Lumh`s s`rbmk hds r`suhtmgds4

@vmhumlbük

 

Vmrbmkt`s g` hm tâlkblm Bklhubr tâlkblms ldkgultumh`s g` myugm

Âkmsbs pu`std `k hds gb`r`kt`s ldopdk`kt`s g`h prdirmom

Hds oâtdgds `oph`mgds `k hms gb`r`kt`s odgmhbgmg`s

Ur`s`ktmr tâlkblm ldonbkmgm ldk dtrms

Odgmhbgmg g` trmtmob`ktd

 

\b uk prdnh`om tb`k` sdhulbük, ´Umrm qu` t` pr`dlupms4 R sb kd tb`k` sdhulbük, ´Umrm qu` t`  pr`dlupms4