Algebra 2 Ejercicios Resueltos

 

Enjldre OO Eatvofef 5 Enucmg8 Iremag H`g H`gmeem meem Qenezer Qenezer.. Aerrlre8 Lf. sla. lm celcåtae. Fgalml8 Ejustme Teõe.

 

Omrgfuaaogm   Lm nes sojuolmtls foepgsotoves vgy e lmigaercl lm lxpnoaer tgfg ng mlalserog pere tlmlr ume sgnofe desl pere lmtlmflr ne tlgrãe fl ngs agmhumtgs. Flsfl sus lnlclmtgs, tlgrãe, y enjumgs lhlcpngs verogs agm sus rlsplatoves lxpnoaeaogmls agm ne iomenofef fl ngjrer qul ln nlatgr agcprlmfe ln tlce. @l tgcefg agcg rlilrlmaoe y eyufe enjumgs tlxtgs y voflgs lmagmtrefgs lm omtlrmlt. Qo dolm ln sgitwerl pgwlr pgomt mg ls co pumtg iulrtl, omtlmterl rlfeater lstl fgauclmtg fl ne clhgr igrce pgsodnl. Flherl ne dodnogjreiãe y cetlroen utonozefg lm ne untoce pejome.

 

Flimoaoñm fl agmhum agmhumgs8 gs8  

\m „agmhumtg– ls um jrupg fl lnlclmtgs u gdhltgs lsplaoioaefgs lm ten igrce qul sl pulfl eiorcer agm alrtlze so auenquolr gdhltg fefg plrtlmlal g mg e ne ejrupeaoñm. [ere flmgter e ngs agmhumtgs, sl usem nltres ceyøsaunes.   Auemfg um lnlclmtg „P– plrtlmlaolmtl e um agmhumtg agmhumtg „E–, lstl sl lxprlse fl igrce socdñnoae agcg8 „P ∀ E– („P– plrtlmlal e „E–).   Lm aesg fl qul um lnlclmtg „_– mg plrtlmlzae e lstl coscg agmhumtg sl utonoze ne mgteaoñm8 „_ ∏ E– („_– mg plrtlmlal e „E–)

 

Igrces fl lmumaoer um agmhumg8 agmhumg8 Lxoslm auerg grces fl lmumaoer e ngs agmhumgs, nes proclres 4 ecdoïm sl nes agmgalm agcg „fllrcomeaoñm–, lses sgm nes sojuolmls8 [gr lxlmsoñm g lmuclreaoñm8 ngs lnlclm lnlclmgs gs fln agmhumg sl flsarodlm lsemfg lmalrrefgs lmrl nnevls nnevls y slperefgs pgr agces. Lhlcpng8 E3{numls, cerls, coïragnls} Lm lsl aesg ln agmhumg slroe „E– y ngs lnlclmgs slroem ngs fães.

4W [gr agcprlmsoñm8 ngs lnlclmgs sl fllrcomem e revïs fl ume agmfoaoñm ne auen lse lsednlaofe lmrl nnevls. Lhlcpng8 E3{foes fl slceme}

 

Gtrg lhlcpng slroe8  E 3 {P/P l M2 < > P > ?} Fgmfl ln sãcdgng „/– sojmoioae „ten qul– g „plrg– y su iumaoñm ls ne fl lstednlalr ne agmfoaoñm fln lnlclmtg „x–. Ne lxprlsoñm sl pgfrãe trefuaor agcg 8 ln agmhumtg „E–, ls ojuen en lnlclmtg „P– ten qul ln lnlclmtg „P– plrtlmlal e ngs møclrgs meturenls y ls ceygr qul < y clmgr qul ?.

Ls flaor, flaor, ln lnlclmtg P tolml qul slr sl r um muclrg meturen, y eflcås slr ceygr qul < y clmgr qul ?, lstgs pgfrãem slr ln 9,: u 0 ye qul aucpnlm agm ne agmfoaoñm qul ln agmhumtg cl pofl.

 

1W Foejreces fl Ylmm8 Qgm rljogmls alrrefes qul sorvlm pere vosuenozer ln agmtlmofg fl um agmhumtg g nes rlneaogmls lmtrl agmhumtgs. 6W Flsaropaoñm vlrden8 Ls um lmumaoefg qul flsarodl ne aereatlrostoae qul ls agcøm pere ngs lnlclmtgs. Lhlcpng8 pere ln sojuolmtl lhlcpng userlcgs nes nltres vgaenls y nes lxprlserlcgs clfoemtl tgfes nes igrces emtlrogrclmtl lxpnoaefes. [gr flsaropaoñm vlrden8 „ln agmhumtg fl nes nltres vgaenls–

[gr lxtlmsoñm8 Y 3 {e,l,o,g,u} Lstgs slroem ngs lnlclmtgs fln agmhumtg fl nes vgaenls [gr agcprlmsoñm8 Y3 {x/x ls ume vgaen} P fldl slr ume vgaen.

 

[gr foejrece fl Ylmm8

 

Anesls fl agmhumgs8 agmhumgs8 Ngs agmhumtgs tecdoïm tolmlm mgcdrls lsplaãioags, lstgs pulflm slr ngs sojuolmtls8

Agmhumtg iomotg8 Qgm equlnngs auygs lnlclmtgs pulflm slr agmtefgs y qul tolmlm iom. [gr lhlcpng8  E 3 {5,4,1,6,…59} Ln agmhumtg „E– tolml 59 lnlclmtgs. Qu aerfomen slroe m(E)359

 

Agmhumtg omiomotg8 sgm equlnngs ngs auenls mg tolmlm iom y sus lnlclmtgs mg pulflm slr agmtefgs, ls flaor, flaor, su aerfomenofef mg lste fliomofe. Lhlcpng8  E3 {9,:,0,?,…} Agmhumtg „E– pgsll ngs møclrgs flsfl ln 9 `este ln omiomotg.

Agmhumtg umoterog8 ls equln qul sgneclmtl pgsll um ømoag lnlclmtg. Lhlcpng8  E3 {4} Agmhumtg „E– pgsll um umoag lnlclmtg. Qu aerfomen slroe m(E)35 m(E)35 (umg ye qul ls sgng sgng um lnlclmtg)

 

Agmhumtg veaãg g mung8 ls equln agmhumtg qul mg pgsll momjøm lnlclmtg, sl pulfl fliomor agm ln sãcdgng „ ω– g agm „{ }–, plrg hecås ω

 }–. –. „{  } Lhlcpng8  E3 ω  E3 { }  E3 {x/x sgm emocenls qul pulflm agcumoaersl agcumoaersl clfoemtl ln `edne} Agmhumtg umovlrsen8 sl ng agmgal agcg agmhumtg fl rlilrlmaoe, ls equln qul agmtolml tgfgs ngs lnlclmtgs qul vem e slr gdhltg fl mulstrg lstufog. Ql flmgte pgr \, y sl ng rlprlslmtere jråioaeclmtl clfoemtl um rlatåmjung. Lhlcpng8 \3 {x/x sgm ngs fães fl ne slceme} \3{x/x slrls vovgs lm ln umovlrsg}

 

Agmhumtgs ojuenls8 sl agmsoflre qul fgs agmhumtgs a gmhumtgs sgm ojuenls so tolmlm ngs coscgs lnlclmtgs som ocpgrter ln grflm lm ln qul sl lmaulmtrlm. Lhlcpng8 Fgs ngs agmhumtgs  E 3 { 1, 6,