20 chuyen de bd toan 8_chon.pdf

7/29/2019 20 CHUYEN DE BD TOAN 8_Chon.pdf

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[rugd ta tng Nbyapjh JXJ [rg [ejg 9:68';89:::

Heuyg mj kgdEh sjgedjj bp 5 6

=9 heuyg mj k-gdEH XJGE DjJ [NG 5

6' YEG [HE F [EH [EGE GEG [=' [GE HEJF E@[ NJ \J F [EH8' HH MJ [NG \ X HEJF E[ HF X GDPZG;' YEGD []GE GDEJ@A GDPZ@G0' HFH MFJ [NFG \@ MJ@P [EH EP [


2/104


Heuyg mj kgdEh sjgedjj bp 5 =

HEPZG

YEG [HE F [EH [EGE GEG [J' [HE A[ EGD [ [EGE GEJP EGD [3

ge b m sugd3

/ f teh l%x* h gdeja eu t te h kgd p.q trngd p b h hf e s t kn" q b h kgd hf e

s hfn get

/ Gu l%x* h tgd hh e s mgd 9 te l%x* h at geg t b x 6

/ Gu l%x* h tgd hh e s hf hh egd t mh heg mgd tgd hh e s hf hh egd t mh b te l%x*

h at geg t b x / 6

/ Gu f b gdeja gduyg hf l%x* v l%6*? l%! 6* oeh 9 tel%6*

f ! 6v

l%!6*

f / 6u b s gduyg' gefge

hegd bnj tr gdeja b h hf e s t kn

6' \ k 63 8x= 5x / ;

Hhe 63 [he egd t te =

8x= 5x / ; 1 8x=


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\ = = == 0 % = 6* ; % 6* ; 9x x x x x vj aj x gg oegd peg the h tege

geg t gf

\ k ;3 x8 / 0x= / 5x / ;

Geg xt3 [gd hh e s hf hh egd t mh heg mgd tgd hh e s hf hh egd t mh b gg f

teh h at geg t b x / 6

x8 / 0x= / 5x / ; 1 %x8 / x= * / %;x= / ;x* / %;x / ;* 1 x=%x / 6* / ;x%x / 6* / ;%x / 6*

1 %x / 6*%x=

/ ;x / ;* 1 %x / 6*%x / =*=

\ k 03 l%x* 1 x0 =x; / 8x8 ;x= / =

[gd hh e s mgd 9 te gg f teh h at geg t b x 6" hejf l%x* hen %x 6* tf h3

x0 =x; / 8x8 ;x= / = 1 %x 6*%x; ! x8 / =x= ! =x ! =*

\ x;

! x8

/ =x

=! =

x

! = oegd h gdeja gduyg hgd oegd h gdeja eu t gg oegd peg the

h gf

\ k


4/104


Heuyg mj kgdEh sjgedjj bp 5 ;

1 %x=

/ x / 6*_%x0

x;

/ x=

x* / %x8

x=

* / 6Q 1 %x=

/ x / 6*%x0

x;

/ x8

x / 6*

Dej ge3

Hh f teh h kgd x8a / 6 / x8g / = / 6 ge3 x4 / x= / 6 ? x4 / x0 / 6 ? x5 / x; / 6 ?

x0 / x / 6 ? x5 / x / 6 ? u h geg t heugd b x= / x / 6

JJJ' [ MJG YE3\ k 63 x%x / ;*%x /


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f8

/ m8

1 %f / m*_%f m*=

/ fmQ 1 a%g=

/= =a ! g

;*' [f h3

H 1 %a / h*8

;'8 =

8 = =a / 8ag ;h 8h%a ! g *;

1 8% ! h8 /ah= ag= / hg=*

1 8_h=%a ! h* ! g

=%a ! h*Q 1 8%a ! h*%h ! g*%h / g* 1 8%f / m ! h*%h / f ! m*%h ! f / m*

J\' YEGD YEY E X M[ GE3

\ k 63 x; !


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Heuyg mj kgdEh sjgedjj bp 5


7/104



HEPZ@G @ =

[GE HEJF E@[ NJ \J F [EH

F' Kfgd 63 [a k huf pe`p hejf af oengd teh ej`g pe`p hejf6' f teh hejf hn kfgd x f %f bf efgd*

f* ge b Mku %M znut" 6489 6458*3

Xn k trngd pe`p hejf f teh l%x* hen ge teh x f mfgd djf tr huf l%x* tfj x 1 f

[f hn3 l%x* 1 %x f*' V%x* / r

fgd teh ugd vj anj x g g vj x 1 f" tf hn

l%f* 1 9'V%f* / r efy l%f* 1 r

[f suy rf3 l%x* hejf e t hen x f l%f* 1 9m* l%x* hn tngd hfh e` snmfgd 9 te hejf e`t hen x 6

h* l%x* hn tngd hfh e` sn huf efgd t mfh hefg mfgd tngd hfh e` snhuf hfh efgd t mfh b` te hejf e`t

hen x / 6

\ ku 3 Oengd bfa pe`p hejf" efy x`t x`a F 1 x8 :x= /


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E shf fteh hejf

E s te =hf f tehm hejf

/E s te6f teh mhejf

f

[ %6* vf %=* suy rf f 1 8" m 16 g`g tf h k bf 8x / 6

Dej ge3

fg mg hejf e t hen f m %f !m*

fg / mg % g b * hejf e t hen f / m %f !m*

\ ku =3 [a k huf hfh pe`p hejf

f* x;6 hejf hen x= / 6

m* x=4 / x: / x8 / x hen x= 6

h* x:: / x00 / x66 / x / 4 hen x= / 6

Djfj

f* x;6 1 x;6 x / x 1 x%x;9 6* / x 1 x_%x;*69 6Q / x hejf hen x; 6 k x g`g hejf hen

x= / 6 k x

m* x=4 / x: / x8 / x 1 %x=4 x* / %x: x* / %x8 x* / ;x

1 x%x=< 6* / x%x5 6* / x%x= 6* / ;x hejf hen x= 6 k ;x

h* x:: / x00 / x66 / x / 4 1 x%x:5 / 6* / x%x0; / 6* / x%x69 / 6* =x / 4

hejf hen x= / 6 k =x / 4

M' X n EN]G

6' X n

ta o t quf huf pe p hejf l%x* hen x f

%f bf efgd sn*" tf s kugd s n enrgG u f teh m hejf bf f9x

8 / f6x= / f=x / f8"

f teh hejf bf x f tf h tegd bf

m9x= / m6x / m=" k r te tf hn

\ ku3

f teh m hejf3 x8 !0x= / 5x ;" f teh hejf x =

[f hn s n

6 ! 0 5 ! ;

= 6 =' 6 / %! 0* 1 !8 ='%! 8* / 5 1 = r 1 =' = /%! ;* 1 9

r1 fm= / f8

f8

m= 1 fm6/ f=m61 fm9/ f6

f=f6

m9 1 f9

f9

f


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Heuyg mj kgdEh sjgedjj bp 5 :

\fy3 x8 !0x= / 5x ; 1 %x =*%x= 8x / =* / 9 bf pe`p hejf e t

=' Fp kugd s n Enrg tge djf tr huf f teh tfj x 1 f

Djf tr huf l%x* tfj x 1 f bf snk huf pe p hejf l%x* hen x f

6' \ ku 63

[ge djf tr huf F 1 x8 / 8x= ; tfj x 1 =969

[f hn s n3

6 8 9 !;

f 1 =969 6 =969'6/8 1 =968 =969'=968 / 9

1 ;9;


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8' \ ku 83 Hegd ajge rfgd

l%x* 1 x:: / x55 / x44 / ''' / x66 / 6 hejf e`t hen d%x* 1 x: / x5 / x4 / ''''/ x / 6

[f hn3 l%x* d%x* 1 x:: x: / x55 x5 / x44 x4 / ''' / x66 x / 6 6

1 x:%x:9 6* / x5%x59 6* / ''''/ x%x69 6* hejf e t hen x69 6

Af x69 6 1 %x 6*%x: / x5 / x4 /'''/ x / 6* hejf e`t hen x: / x5 / x4 /'''/ x / 6

Xuy rf l%x* d%x* hejf e t hen d%x* 1 x: / x5 / x4 /'''/ x / 6

G`g l%x* 1 x:: / x55 / x44 / ''' / x66 / 6 hejf e`t hen d%x* 1 x: / x5 / x4 / ''''/ x / 6

;' \ ku ;3 HA]3 l%x* 1 %x= / x 6*69 / %x= ! x / 6*69 = hejf e`t hen d%x* 1 x= x

f teh d%x* 1 x= x 1 x%x 6* hn = gdej a bf x 1 9 vf x 1 6

[f hn l%9* 1 %!6*69 / 669 = 1 9 x 1 9 bf gdej`a huf l%x* l%x* hef tef sn x

l%6* 1 %6=

/ 6 6*69

/ %6=

6 / 6*69

= 1 9 x 1 6 bf gdej a huf l%x* l%x* hef tef snx 6" af hfhtef sn x vf x 6 oengd hn gefg t heugd" kn n l%x* hejf e t hen x%x 6*

efy l%x* 1 %x= / x 6*69 / %x= ! x / 6*69 = hejf e t hen d%x* 1 x= x

0' \ ku 03 Hegd ajge rfgd

f* F 1 x= x: x6:;0 hejf e t hen M 1 x= x / 6

m* H 1 5x: :x5 / 6 hejf e t hen K 1 %x 6*=

h* H %x* 1 %x / 6*=g x=g =x 6 hejf e`t hen K%x* 1 x%x / 6*%=x / 6*

Djfj

f* F 1 x= x: x6:;0 1 %x= x / 6* %x: / 6* %x6:;0 x*

[f hn3 x= x / 6 hejf e t hen M 1 x= x / 6

x: / 6 hejf e`t hen x8 / 6 g g hejf e t hen M 1 x= x / 6

x6:;0 x 1 x%x6:;; 6* hejf e t hen x8 / 6 %hugd hn gdej`a bf x 1 ! 6*

g`g hejf e t hen M 1 x= x / 6

\fy F 1 x= x: x6:;0 hejf e t hen M 1 x= x / 6

m* H 1 5x: :x5 / 6 1 5x: 5 ! :x5 / : 1 5%x: 6* :%x5 6*

1 5%x 6*%x5 / x4 / '''/ 6* :%x 6*%x4/ x< / '''/ 6*

1 %x 6*%5x5 x4 x< x0 x; x8 x= x 6*

%5x5 x4 x< x0 x; x8 x= x 6* hejf e t hen x 6 v hn tngd e` snmfgd 9

suy rf %x 6*%5x5 x4 x< x0 x; x8 x= x 6* hejf e t hen %x 6*=


11/104



h* f teh hejf K %x* 1 x%x / 6*%=x / 6* hn mf gdej a bf x 1 9" x 1 ! 6" x 1 !6

=

[f hn3

H%9* 1 %9 / 6*=g 9=g ='9 6 1 9 x 1 9 bf gdej a huf H%x*

H%!6* 1 %!6 / 6*=g %! 6*=g ='%! 6* 6 1 9 x 1 ! 6 bf gdej a huf H%x*

H%!6

=* 1 %!

6

=/ 6*=g %!

6

=*=g ='%!

6

=* 6 1 9 x 1 !

6

=bf gdej`a huf H%x*

Anj gdej`a huf f teh hejf bf gdej a huf f teh m hejf pha


12/104


Heuyg mj kgdEh sjgedjj bp 5 6=

HEPZG 8

HH MJ [NG \ X HEJF E[ HF X GDPZGJ' Kgd 63 Hegd ajge qufg e hejf et

6' Ojg teh3

# hegd ajge F%g* hejf et hen at s a tf peg the F%g* tege geg t h at geg t ba enhmj hf a" gu a b ep s te tf bj peg the g tege geg t h hh at gduyg t hgd gefu" rj

hegd ajge F%g* hejf et hen hh s

# He 3

/ \j o s gduyg bjg tjp mfn dj hgd tg tj at mj hf o

/ Oej hegd ajge F%g* hejf et hen a tf xt aj trgd ep v s k oej hejf F%g* hen a

/ \j aj s gduyg f" m v s t gejg g te3

=' Hh mj tng

Mj 63 hegd ajge rgd

f* =06

! 6 hejf et hen 4 m* =49 / 849 hejf et hen 68

h* 646:

/ 6:64

hej et hen 65 k* 8


13/104



f* g0

! g 1 g%g;

! 6* 1 g%g ! 6*%g / 6*%g=

/ 6* 1 %g ! 6*'g'%g / 6*%g=

/ 6* hejf et hen < v

%g ! 6*'g'%g/6* b the hf mf s t gejg bjg tjp gg hejf et hen = v 8 %#*

At oeh g0 ! g 1 g%g= ! 6*%g= / 6* 1 g%g= ! 6*'%g= ! ; / 0* 1 g%g= ! 6*'%g= ! ; * / 0g%g= ! 6*

1 %g ! =*%g ! 6*g%g / 6*%g / =* / 0g%g= ! 6*

\ %g ! =*%g ! 6*g%g / 6*%g / =* b the hf 0 s t gejg bjg tjp gg hejf et hen 0

0g%g=

! 6* hejf et hen 0Xuy rf %g ! =*%g ! 6*g%g / 6*%g / =* / 0g%g

=! 6* hejf et hen 0 %##*

[ %#* v %##* suy rf pha

m* t F 1 g; !69g= / : 1 %g;!g=

* ! %:g=

! :* 1 %g=

! 6*%g=

! :* 1 %g ! 8*%g ! 6*%g / 6*%g / 8*

\ g b gg t g 1 =o / 6 %o S* te

F 1 %=o ! =*'=o'%=o / =*%=o / ;* 1 6


14/104


Heuyg mj kgdEh sjgedjj bp 5 6;

Mj ;3 Hegd ajge rgd F 1 68 / =8 / 88 / '''/ 6998 hejf et hen M 1 6 / = / 8 / ''' / 699

Djj

[f h3 M 1 %6 / 699* / %= / ::* / '''/ %09 / 06* 1 696' 09

hegd ajge F hejf et hen M tf hegd ajge F hejf et hen 09 v 696

[f h3 F 1 %68

/ 6998* / %=

8/ ::

8* / ''' /%09

8/ 06

8*

1 %6 / 699*%6=

/ 699 / 699=

* / %= / ::*%==

/ =' :: / ::=

* / ''' / %09 / 06*%09=

/ 09' 06 / 06=

* 1 696%6=

/

699 / 699=

/ ==

/ =' :: / ::=

/ ''' / 09=

/ 09' 06 / 06=* hejf et hen 696 %6*

Bj h3 F 1 %68 / ::8* / %=8 / :58* / ''' / %098 / 6998*

Aj s egd trngd gdnh u hejf et hen 09 gg F hejf et hen 09 %=*

[ %6* v %=* suy rf F hejf et hen 696 v 09 gg F hej et hen M

Mj tp v ge

Hegd ajge rgd3

f* f0 f hejf et hen 0

m* g8 /


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Oegd o peg e s hf oefj trjg Gjutg te ;5 s egd u hef tef s 0 vj s a bg eg enh

mgd 8 gg u hejf et hen 08 1 6=0" efj s egd tjp te`n309';:

=' 0

=! 09'0 hgd hejf et hen 6=0 " s

egd huj hgd b 6

\y3 =699 1 M%6=0* / 6 gg hejf hen 6=0 te k 6

Mj =3\jt s 6::06::0 tege tgd hf hh s t gejg ' [gd hh bp pegd hejf hen < te k mfn geju>

Djj

t 6::06::0 1 f 1 f6 / f= / / fg'

Dj 8 8 8 86 = 8 g

X f f / f / '''/ f 1 8 8 8 86 = 8 g

f f / f / '''/ f / f ! f

1 %f68

! f6* / %f=8

! f=* / / %fg8

! fg* / f

Aj ku gdnh u hejf et hen < v aj ku gdnh b the hf mf s t gejg bjg tjp' He hg ta s k

oej hejf f hen

k* h 8 he s" hh he s h te djgd gefu>

Mj =3 H mfn geju s t gejg h ; he s bp mj hh he s 6" =" 8 mjt rgd s hejf et hen :

Mj 83 [rg trfgd v h < gd o tegd gd v 0 gd o ga gdfgd j at ht gefu' Ej trg

trfgd v h mfn geju ege he get

x

yM0M;M=M6

F0F;F8 F

20 chuyen de bd toan 8_chon.pdf

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