2 - Alg - 5° PRE - Cap16 - 2021
August 2, 2022 | Author: Anonymous | Category: N/A
Short Description
Download 2 - Alg - 5° PRE - Cap16 - 2021...
Description
Êmihorj
Iuäj Jajnådeaj SE - Aehfaejs (\_H-?:)
Ajpätumk
:3
QEQ^HDJQ NH HAXJAEKFHQ
DJ_AK ^HÑ_EAK QEQ^HDJQ NH HAXJAEKFHQ Nhcefeaeñf
Hs jquhm akfbuftk nh nks k dês haujaekfhs quh sh vhreceajf pjrj mks desdks vjmkrhs nh sus efañifetjs. \kr hbhdpmk, mjs haujaekfhs2 1 x 8y :1 9 x ?y 1
^kdjfnk mks hbhdpmks jfthrekrhs, sh tehfh2 Nhm predhr sesthdj2 1 x 8y :1 9 x ?y 1
h shiufnk uf sesthdj2 st Nhm > x y z :? 1 x y z 5
Qh vhreceajf pjrj x 4 : h y 4 ?.. aek Ktrk hbhdpmk, mjs haujaekfhs2 > x y z :? 1 x y z 5
Qh vhreceajf pjrj2
x 1,
y :,
z :
x 1, x 1,
y y ‑ 5 z ? x ?y ‑ 1z >
Jndeth uf akfbuftk skmuaeñf nh efcefetks hmhdhftks, hm aujm hs2 Q4 {(?, :, z 5
FK skf efnhphfnehfths 3 x > y 0 z : 0
yj quh sh audpmh2
1 3
? >
> 0
Nh jauhrnk jm fòdhrk nh haujaekfhs efnhphfnehfths y nh efañifetjs, hstjs puhnhf shr2
Êmihorj
Iuäj Jajnådeaj SE - Aehfaejs (\_H-?:) :.
Qesthdjs akfsesthfths
?.
Qesthdjs efakfsesthfths
Qkf jquhmmjs quh jndethf akdk akfbuftk skmuaeñf, hm akfbuftk FK vjaäk.
Qkf jquhmmks auyk akfbuftk skmuaeñf hs hm vjaäk. Hf hsth ajsk, fk sh puhnh hstjomhahr ufj rhmjaeñf hxpmäaetj hftrh hm fòdhrk nh haujaekfhs EFNH\HFNEHF^HQ y hm fòdhrk nh efañifetjs.
j) Nhthrdefjnks
F.² nh haujaekfhs 4 F.² nh efnhphfnehfths efañifetjs
\kr \kr hbhdpmk
\kr hbhdpmk hf hm sesthdj sesthdj22
Hm sesthdj dkstrjnk2
1 x > y : :
x + + 1y 4 8 ? x + + 3y 4 9
Qh audpmh2
? x 8y 0
(?) haujaekfhs efnhphfnehfths 4 (?) efañifetjs
o) Efnhthrdefjnks
.² nh F.² nh haujaekfhs = F.² ef etj efnhphfnehfths efañifetjs
d 2 \kr hbhdpmk hf hm hm sesthdj sesthdj2
\kr hbhdpmk hf hm sesthdj sesthdj22 x y 1 x y : Qh audpmh2 1 x y 9
(1) haujaekfhs efnhphfnehfths 6 (?) efañifetjs
Hss nhaer, nhaer, mmjs haujaekfhs j fk skf efnhphfnnehfths. e s.
1 x + + y 4 9 ? x ‑ ‑ y 4 1 x + + 1y 4 >
(?) haujaekfhs ek efnhphfnehfths hf = (1)) efañifetjs
F.² nh haujaekfhs 6 efañifetjs F.² nh efnhphfnehfths
3
Hmm sesthdj s j skorhnhthrdefjnk2
Qh audpmh2 m Q
a) Qkorhnhthrdefjnks
?
Ktrk tr hbhdpmk hd
? x y z 8 1 x y z >
hs EFAKFQEQ^HF^H, phrk thñreajdhfth ffkk sshh jjbustj ustj j hhstj s ckrdj nh amjseceajaeñf. hr Nhoenk j quh sh vhreceaj mj prkpkraekfjmenjn2 : 1
tjdoeåf hs EFAKFQEQ^HF^H. Kosårvhsh quh mjs haujaekfhs skf nks j nks, efnhphfnehfths.
_hskmuaeñf nh uf sesthdj nh haujaekfhs
Hs hm prkahsk nh trjfsckrdjaekfhs suahsevjs nh mjs haujaekfhs nhm sesthdj, hf ktrjs hquevjmhfths quh phrdetjf nhsphbjr mks vjmkrhs nh mjs efakifetjs. Jfêmeses nh mks sesthdjs nh haujaekfhs mefhjmhs
Nhfkdäfhsh sesthdj mefhjm j jquhm auyjs haujaekfhs akfckrdjfths skf tknjs nh predhr irjnk.
11
Êmihorj
Iuäj Jajnådeaj SE - Aehfaejs (\_H-?:)
\jrj rhskmvhr uf sesthdj mefhjm, sh utemezjf vjreks prkahnedehftks, tjmhs akdk2
Hm arethrek nh mj sustetuaeñf Hm arethrek nh mj eiujmjaeñf Hm arethrek nh mj rhnuaaeñf Hm arethrek nh mjs irêceajs
Hbhdpmk hxpmeajtevk
_hsuhmvj hm sesthdj mefhjm2 ? x + + 8y 4 :3 9 x ‑ ‑ 1y 4 :8 Ajmaumhdks pkr shpjrjnk mks nhthrdefjfths2
^jdoeåf prkahnedehftks dua`k dês prêateaks2 prê ateaks2 _himj nh Ohzkut, nh mks akhceaehfths efnhthrdefjnks. _himj nh Arjdhr, nh mks nhthrdefjfths. _himj nh dumtepmeajaeñf hf aruz, pjrj sesthdjs mefhjmhs hsphaejmhs.
s
? 9
x
:3 :8
y
? 9
U nh mks rhaursks nh mjs djthdêteajs suphrekrhs2 suphrekrhs2 Hm arethrek jfjmäteak nh mjs djtreahs. ks prkahh \jrj fuhstrks cefhs utemezjrhdks sñmk mks nedehftks hmhdhftjmhs.
Qh kotehfhf j pjrter nh2
x
x
y
h
s
y
s
nkfnh mks nhthrdefjfths sh nh nhcefhf cefhf jsä2 s x y
j:
o:
j?
o?
a: a?
o: o?
j:
a:
j?
a?
j:o? ‑ j?o: a:o? a ?o: j:a ? j?a:
8 1 :3 :8
:3)) (‑1 (‑1)) ‑ (:8 (:8)) (8) (8) ‑: ‑:?1 ?1 (:3
(:8)) ‑ (9 (9)) (: (:3) ‑0 ‑0? ? (?) (:8
x ::?1 1 s >: y 0? y ? s >: \krr mk tjftk, k, hm akfbuft akfbuftk kfb k skmuae skmuaeñf ñf shrê2 x
k thdj meMks vjmkrhs nh mjs efakifetjs x x h y nhm sesthdj fhjm jnbuftk2 j: x + + o:y 4 a: j? x + + o?y 4 a?
(? (?)) (‑ (‑1) ‑ (9) (9) (8) ‑> ‑>: :
\kr kr Arjdhr sh tehfh2
h nh ? efañifetjs2 ñ s2 Hstunek nhm sesthdj mefhjm _himj nh Arjdhr
8 1
Q4 {(1, ?)} kpee kp \rkpehnjnhs nh prkpkraekfjmenjn y jfêmeses irê ceak ceak nh mk mks s se sest sthd hdjs js me mefh fhjm jmhs hs nh ? ef efañ añif ifet etjs js
Qh tehfh hm sesthdj mefhjm2 M 2 j x + o y 4 a : 2 j: x + o: y4 a : M ? ? ? ? nkfnh M : y M ? skf mjs haujaekfhs ajrthsejfjs nh nks rhatjs uoeajnjs hf hm pmjfk PKU PKU.. Qe åstjs sh efthrshatjf sh tehfh2 U
M :
y
K
1>
\( x xy
...
1 x 1
?
Qudjfnk (?)+(1) ? z 8 z
_hhdpmjzjfnk hf (?) sh s tehfh2
8
?
1 8 ? ‑ y ? ? 1 8 ‑ ?y ? ?
Qudjfnk jf (:)+(?)+(1)2 )+ x + y + z 4 3 _ jz _hhdpmjzjfnk2 ( x x + y + z)y 4 3? 4 13 _ptj.2 H
1.
Nhthrdefh hm vjmkr nh j pjrj quh x vjmij vjmij hm trepmh nh y hf hm sesthdj 1 x ?y j ? ? x ‑ 1y ?j ‑ ?
`jmmh hm vjmkr nh ( x x + y + z)y. (XFDQD ? ‑ g)y 4 :
\jrj quh q thfij i efcefetjs skmuaekfhs. O) ‑ : N) ?
...(? ..(?)) y 3 ....
9.
:<
O)
:8
A)
?<
N)
1<
Bkshmetk akdprj ( x x + 8) aujnhrfks akf hm prhaek ufetjrek nh 3 skmhs7 y hm rhsumtjnk nhm sesthdj2 1 > :,1...(:) x : y 1 > 8 : ...(?) x : y 1 1
><
J) 5
J) ‑ ? A : A)
J)
O) ?0 >< skmhs N)
@jmmh hm vjmkr nh j hf hm sesthdj > x + + y 4 j ‑ ? ...(:) x ‑ ‑ 8y 4 ?j + : ...(?) \jrj quh hm vjmkr nh x shj shj hm trepmh nh y
hm sesthdj2 Nhthrdefh hm vjmkr nhh y hf hm
Qe åm pjij akf uf oemmhth nh :0: ...(E) ...(EE) x xy y :1
J) 1< A) 8<
O) >< N) 3<
5.
Muhik nh rhskmvhr hm sesthdj
x ? ? : ...() y ? x y : x ? x ? ...() y 1 y 1
@jmmh hm vjmkr nh J) A) ?>
^
:y + z 4 5 8 x + + ?y + 1 z 4 5 . . Ajmaumh hm vjmkr nh ^ 4 x y z.
J) ‑? A) :
O) ‑: N) ?
x y x ? y ? :< .
O) N) 81
>:
Êmihorj
Iuäj Jajnådeaj SE - Aehfaejs (\_H-?:)
JQHQK_ÄJ :.
J) j? + jo A) o? ‑ jo
Ajmaumh x y se x + +y
‑ y 4 :,8 + x ‑ 1 ?
? x + + y + 1 x ‑ ‑ ?y 4 ? 8 >
J) : A) :3 ?.
O) ? N) 1?
8.
»Auêftks fehtks tehfh hm J Jouhmk Jrquädhnhs; d J) ? A) 8
O) 1 N) 9
1.
_hsuhmvj
1( : ?)d ?(: ?)f 3 ?(: ?)d 1(: ?)f 3
shj akdpjteomh efnhthrdefjnk efnhthrdefjnk.. J) ‑ : O) ‑ :1 ? 9 A) N) < ?
3. 3
@jmmh hm vjmkrr nh d pjrj rj quh hm sesthdj
9..
(j ‑ o) x x + + (j + o)y 4 ? j? ‑ o?
Nå akdk rhspuhstj hm vjmkr nh xy.
>?
fa fa h . shj efakfsesthfth. J) J :? A) ‑ :<
O) :< N) 1
\kr mj akdprj nh (f+0) djfzjfjs sh pjij ? skmhs. Qe sh vhfnh (d ‑ :) djfzjfjs pkr 1 skmhs. »Auêftjs djfzjfjs `jorê quh vhfnhr pjrj ijfjr 3 skmhs; Qjoehfnk quh f y d skf hm dhfkr djykr vjmkr, rhsphatevjdhfth7 rhsphatevjdhfth7 quh `jahf quhy hm sesthdj2
_hsuhmvj hm sesthdj (j + o) x x ‑ ‑ (j ‑ o)y 4 >jo
8 x + + dy 4 5 (d + 99) x x + + 3y 4 3d
>.
(d + :) x x + + >y 4 1 3 x + + (d ‑ :)y 4 j ‑ 1
h efnequh hm vjmkr nh ^ 4 >(d ‑ f). J) < O) 0 A) ?> N) 1?
@jmmh hm djykr vjmkr nh j + d pjrj quh hm sesthdj
Hm fòdhrk nh fehtks nhm jouhmk Jrquädhnhs hstê njnk pkr hm vjmkr nh x muhik muhik nh rhskmvhr hm sesthdj2 1 :< x ? y 8 1 ...(E) 5 > :: ...(EE) y 8 x ? 8
O) j? ‑ jo N) j? ‑ o?
8 x 9 jy j 5 7 nkfnh j < x y 8 8 Fk thfij skmuaeñf òfeaj.
J) 1< A) 3>
O) 13 N) 9?
Êmihorj
Iuäj Jajnådeaj SE - Aehfaejs (\_H-?:) 0.
\ehrk hs uf jmudfk efirhsjfth nhm aeamk ? ? ? :8 ? x y > ? x y 1 > x y ...() »Auêftk rhaeoeñ \ehrk akdk prhdek;
J) ?8< nñmjrhs A) ??1 nñmjrhs
O) ?11 nñmjrhs N) ? N
: N) :3
Hm pjr ( x x 1 x y x y 1 ? ? x y x y
Nå hm vjmkr nh x .
? : ‑ ? x + 1 : + ? y 4 3
?.
1.
...(E) ...(EE)
O) 1 N 8 N)
@jmmh hm vjmkr nh d pjrj quh u hm sesthdj h 8 x + + dy 4 5 (d+9) x x + 3y 4 3d shj efakfsesthfth J) 9 A) :<
>>
O) 5 N) ‑ :<
O) 1 ? N) 1
Nhm sesthdj x + ?y ‑ z 4 ? ? x ‑ y + 1 zz 4 5 ? x ‑ y + z 4 1 Nå hm vjmkr mkr nh x. J) 8 A) ?
y
J) ? A) >
J) ? 1 A) ?
...(?)
O) > N) :
View more...
Comments
