Problemas Resueltos Capitulo Iv

 

9.  9.  Xb iblkko nh ]owkibn fobslsth hb ub bõfkho nh glhrro (¸r 1 =333) nh 8 Zfa =Q nh shfflöb y >3 ZfaQ nh nléahtro ahnlo. Hk momlbino fobsti nh 93 vuhktis por fhbtáahtro. Gikkir ki rhkuftibfli nhk bõfkho, ki `uhrzi aidbhtoaotrlz quh pronufh ubi forrlhbth nh 3.= ZIQ ik flrfukir por ki momlbi y hk `kueo hb hk bõfkho.

9  18Ô93∝    933  . 1 3.>   1=1=   

M

18 Ô r

L

L

  1 >33 193  Ô= >33        Iv ℚ 1  1 =333(>Ô933.> ∝)Ô(8Ô93∝) 19Ô93   ZTmQ    1  1 >33 Ô 3.= 1 73 I v  73 ∝   1∈ℚ   ↝ ∈ 1 9Ô93 17Ô93  Tm

=.  =.  Xb hkhftrolaéb fobsti nh ub bõfkho nh glhrro ronhino nh ubi momlbi nh 833 hsplris por ki quh flrfuki ubi forrlhbth nh 3.9 ZIQ. Vl hk `kueo aidbìtlfo hs nh 9.=8 Ô 93 -6  ZTmQ. ¿Fuék hs ki rhkuftibfli nhk bõfkho?

833Ô3.9 1>Ô93   ZI v Q  1∈ℚ ↝ ℚ1 9.=8Ô93 ∝ Tm 6.  6.  Nos bõfkhos aidbìtlfos, nh kis nlahbslobhs y phrahimlklninhs shùikinis hb i `lduri sh fobhftib hb shrlh fob rhsphfto i ki nlrhfflöb nhk fiapo aidbìtlfo ipklfino. ¿Fuék hs ki rhkuftibfli totik?

¸r1033

93 fa

¸r19333 V 1 93 fa

=8 fa

 9   193 Ô 933 19Ô93∝ 

=

 

 1 93  Ô   13.9   :  1 =8  Ô   1 3.==88  

 

 

I v Q  ℚ 1  1 033(>Ô93∝3.9)Ô(9Ô93∝) 19.66Ô93   ZTm 3.=8    Z I v Q  ℚ 1  1 19..90Ô93  Z ZITm ℚ 1  1 033(>Ô939.84 TmQ I v Q     Z I v Q  19.8Ô93∝3.339 Tm )Ô(8Ô93∝)

∝ (8.48Ô93 ) ) ( ∈ ℚ  ℚ 8Ô93   1∈((ℚ  ℚ)   ↝  1  1 1∈ 1 3.848 848 I  833 8.  8.  Nos bõfkhos aidbìtlfos, nh kis nlahbslobhs y phrahimlklninhs shùikinis hb ki `lduri, sh fobhftib hb pirikhko rhsphfto i ki nlrhfflöb nhk fiapo aidbìtlfo ipklfino. ¿Fuék hs ki rhkuftibfli hqulvikhbth? ar 1033

 1 =8  Ô   13.=8 a   1 93   Ô    19Ô93∝ a=   9    1 =3   Ô 933  1=Ô93∝ a=     Z I v Q  16.6=Ô93 ℚ 1  1 033(>Ô933.=8 ∝ )Ô(9Ô93∝ ) Tm 3.=8 ℚ 1  1 13. 1 =>3 I v 

3.= ∝) Ô  1 9Ô93    ZTm  1 =>3 1 9.= ^ ∈ 1 ℚ   ∰ ∈ 1   ↝  1 ∈ 1 ℚ 9Ô93 ∝) 19=33 ZaQ  AIYXLBIV HKÌF^]LFIV5 Ehsõs @rilkh Aori 7.  7.  Hk bõfkho aidbìtlfo aostrino hb ki `lduri tlhbh ubi shfflöb tribsvhrsik ubl`orah lduik i 933 Zfa=Q. Ki momlbi I tlhbh 9333 hsplris, flrfukibno ubi f.f. nh 3.8 ZIQ hb ki nlrhfflöb lbnlfini.

 

Nhthralbir ki forrlhbth L M, piri fobshdulr ub `kueo buko hb hk mrizo fhbtrik. Ki phrahimlklnin rhkitlvi hs ¸r 1 =33.

=

933 fa

]  9

L

+

L

I

BI 19333

]  =

+

M

]  6 +

B9

BM 1=33

83 fa

BILI

`

9

-

 

`

=

+

-

-

-

BMLM

933 fa

(ℚ  ℚ)∈  ℚ∈ 1       ℚ∈  (ℚ  ℚ)∈ 1    Ophribno iamis hfuiflobhs y fobslnhribno quh5

ℚ 1 ℚ : Ю  1Ю . (ℚ  ℚ  ℚ)∈ 1      (ℚ  ℚ  ℚ)∈ 1    ∈ 1 ℚ    ↝ ℚ Zℚ  Q 1       1       ↝  1 =  1 9333Ô3.8 I  =Ô=33 1 9.==88 I 9

=

333 Z I vQ  ℚ 1   1 3.39Ô3.33=8 Tm 3.=Ô933.338 ∝)Ô3.338 Tm ∝ )Ô90046>>  1 (8Ô93 =Ô603 1 99 99.8.844 I I  93.   Ki hstrufturi aidbìtlfi nh ki `lduri hsté `imrlfini 93. `imrl fini fob nos tlpos nh aithrlikhs, fuyis furvis nh aidbhtlziflöb vlhbhb hxprhsinis por kis hfuiflobhs5

 

9.9   :  1 =.9    : I/a   1 8333 =333  99.   Fikfukir ki lbthbslnin L quh nhmh flrfukir por ki momlbi piri pronuflr ub `kueo nh 9.8Ô93 -> ZTmQ, 99. sl ki shfflöb hs ubl`orah y vikh 98 Zfa=Q. 3.= ZaQ

3.> ZaQ

`

L

a

]  9

=

+ B 19>3

-

BL

+ -

]  =

 

=.9     1 =333 

∈ 9.8Ô93∝   ∝ 1 3.9 ^ ↝ 1  1 9.8Ô93 ↝ 8333.9 19.9  ^1833 ZaI Q  ↝ =333.9 1=.9   1933 ZaI Q 

 1   

3.9 1=Ô93∝   Z^ aQ  ↝   1  1 833 I

9.9∈1   1 8333 

  1  1 3.9 19Ô93∝   Z^ aQ   933 I   3.= I v Q   ℚ 1   1 (=Ô93∝ ) Ô (9.8Ô93∝) 1000000.04 ZTm I v Q  ℚ 1  1 (9Ô93∝ ) 3.> 1=00000.04 Z ∝ Ô (9.8Ô93 ) Tm ∝) ) ( ( ∈ ℚ  ℚ ()Ô 9.8Ô93   (ℚ  ℚ)∈ 1  ↝  1  1 1 9 I I  9>3

 

9=.   Hb hk flrfulto aidbìtlfo, ki momlbi nh =333 vuhktis tlhbh ubi forrlhbth nh 93ZIQ. Vupobdi quh 9=. tonis kis riais tlhbhb ubi shfflöb tribsvhrsik nh = Zfa=Q y quh hk aithrlik nhk bõfkho hs glhrro fob ¸r 1 9833. Fikfukh5 i) i)   Ki `uhrzi aidbhtoaotrlz m) m)   Ki rhkuftibfli hb hk bõfkho y hb hk hbtrhglhrro f) f)   Hk `kueo aidbìtlfo

`

a

]  b

93 fa

3.0 fa

9= fa

+ -

9 fa

= fa

 . .. . . .11  1 =333 Ô 93 1 = Ô 93  I v   Iv ℚ 1  1 9833(>Ô933.>6> ∝)Ô(=Ô93∝ ) 199.89==Ô93   ZTmQ     Z I v Q  ℚ 1  1 (>Ô93∝3.330 1=67.46=>Ô93 )Ô(=Ô93∝) Tm  =Ô93  >0Ô93 1 4.