7/30/2019 Alg 04 - DivisionAlgebraica

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www/ghtahokhrti/mbdnspdt/fdg YO[ [rucjbbdHrti y Ghtigtjfh =586

HVJNOH[Y]H3BNIM]H

Urftjfh 5; KJPJVJO HBNIM]HJFH58/Vj ib ristd ki kjvjkjr3

1x;x=x

ogxx=0x9x1x6

=6

=6;9

is3 ' 9x , =/ Ahbbhr 3 g , o

h* = m* = f* 6

k* > i* >

5=/ Io bh kjvjsjo od joixhfth3

fmxhx

mhmfxhmx:x*f=h0!mx=hx=

=

==6=;9

Kitirgjoi ib vhbdr ougrjfd ki3

*h:

h!

f

8I

h* 8 m* 8$= f* 8$6

k* 8$0 i* 8$;

56/ Vjiokd 3{h " m} " sj bh kjvjsjo3

==

=6;

mx*mh!x

mx*mh!x*mh!x

is ixhfth" fhbfubhr ib vhbdr ki3

m6h=

mhmh]

==

h* 8 m* = f* 6

k* 9 i* >

5;/ Fhbfubhr ib vhbdr ki3 h ,m , f , k , i , `" sj si shmi qui io

bh kjvjsjo3

=xxx6

`ixkxfxmxhxx=8

=6

=69;0

si fugpbi qui bds fdi`jfjioti kib fdfjioti iotird kjsgjouyio

ki = io =/ Hkigs bh kjvjsjo hrrdch uo risjkud jnuhb h 6/

h* 0 m* ; f* =

k* = i* ;

59/ Ahbbhr !h , m , g*" sj bh kjvjsjo3

9x>x

m8=hxx8:x;x=x

6

=6;9

ki pdr risjkud 3 gx= , =x 0

h* 5 m* =6 f* ==

k* 8: i* 88

50/ Bh sjnujioti kjvjsjo3

fxhx

hx*8f!fmx*8f!hfx=hmxxh6

=6;9=

hrrdch uo fdfjioti iotird y uo risjkud fuyds fdi`jfjiotis

isto io prdnrisjo nidgtrjfh y prdnrisjo hrjtgtjfh" sino

istd fhbfubhr3

88

8

fm

h=z

h* 8 m* = f* 6

k* ; i* 9

5>/ Fhbfubhr ib risjkud io bh sjnujioti kjvjsjo3

6

66=6;

96x

;=9x*6=99!x696x

h* 6 m* 9 f* >k* : i* 1

51/ Fhbfubhr o sj si shmi qui io bh kjvjsjo3

8ox*8oo!///x*=o6!x*8o=!ox

=6o=o8o

si fugpbi qui 3 : vifis bh sugh ki fdi`jfjiotis kib fdfjioti

is jnuhb h ; vifis ib ristd ki bh gjsgh kjvjsjo/

h* 6 m* 0 f* :k* 8= i* 89

5:/ Kjvjkjr3

x

:x=*6x!9*6x!=*6x!6*6x! =6;9

khokd ib vhbdr kib fdfjioti fuhokd x tdgi ib vhbdr ki ;/

h* 8 m* = f* 6

k* 9 i* 0

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85/ Ahbbhr ib ristd ki bh kjvjsjo3

*=5x:x!

:*;x!*9x!

=

;598

h* x ' 8 m* =x f* 6

k* 0 i* x , 8

88/ Viho bds pdbjodgjds X!x* 7 hx= , mx , x

]!x* 7 gx , o

Ib fdfjioti y ib risjkud rispiftjvhgioti ki bh kjvjsjo

*x!x

xxxx

8

;816==

=6;

Fhbfubhr !h m f* =

h* 8 m* ; f* :

k* 80 i* =9

8=/ Khkh bh kjvjsjo

6

6;=90

;=8

8>=91;

xx

xxxxx

Iouofjhr ib vhbdr ki virkhk ki bhs prdpdsjfjdois sjnujiotis

J/ Vu fdfjioti is x6 , =x= , 8JJ/ Vu ristd is 6x= =x

JJJ/ Bh sugh ki sus fdi`jfjiotis kib fdfjioti is 9h* PP@ m* P@P f* @@P

k* @@P i* PP@

86/Ahbbhr ib vhbdr ki " sj bh kjvjsjo

=6=;

;8=6

=6;9

xxx

xx*f!mxhx

Is ixhfth

h* = m* ; f* 6

k* 6 i* 9

8;/Dmtioir ib ristd ki i`iftuhr bh kjvjsjo jokjfhkh

x

gx*x!*x! g

6=

6==6 ===

Vj ib fdfjioti ivhbuhkd io fird risubth sir 6

h* > m* 1 f* :

k* 85 i* 88

89/Ahbbhr ib risubthkd ki sustjtujrxpdrx , 6 io bh ixprisjo

`!x* 7 =x; x6 =x= , 9x , 8

h* =x; =6x6 , :>x= , 81=x , 868

m* =x; , =6x6 :>x= , 81=x 868

f* =x; =6x6 , :>x= 81=x 868

k* =x; ,=6x6 , :>x= , 81=x , 868

i* =x;

=6x6

, :>x=

, 81=x 868

80/Kitirgjohr bh sugh ki fdi`jfjiotis kib fdfjioti qui si

dmtjioi hb kjvjkjr !;x15 =x>: , x , m* iotri !x 8*

h* 805 m* 80= f* 806

k* 80; i* 809

8>/ Hb kjvjkjr

8

88888=

=8=9;;66==

x

*x!////*x!*x!*x!*x! oo

Jokjfhr ib trgjod jokipiokjioti kib risjkud

h* *! o 8;6

= m* *! o 8;

6

= f* *! o 8=

;

6

k* *! o 8;=6 i*

81/ Ahbbi ib risjkud ki kjvjkjr

=;

111>6;=

=6;9

xx

xxxxx

h* 86x , 0 m* 86x 0 f* 86x , 0

k* 86x 0 i* x

8:/ Fhbfubhr ib vhbdr ki h/m" sj bh kjvjsjo is ixhfth3

66

6;>

=

=6;

xx

xxmxhx

h* 8= m* 6; f* 6=

k* ;6 i* >=

=5/ Fhbfubhr Y , O , [" sj bh kjvjsjo3

6xx=

[OxYxx;x1

=6

=69

kich pdr ristd3 8x=x6=

h* =5 m* == f* =;

k* =1 i* 65

58* I 5=* M 56* I 5;* K 59* F50* H 5>* F 51* F 5:* F 85* M88* M 8=* H 86* H 8;* F 89* K80* F 8>* H 81* F 8:* H =5* F