A L g e b r a belgilar va belgilashlar
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- Bu sahifa navigatsiya:
- Modulli tenglamalar Moduli tenglamalar
- Modulli tengsizliklar Moduli tengsizliklar
- Click here to buy A B B Y Y PD F Transfo
- Irrasional tenglama . Irrasional tenglamalarni
- Irrasional tengsizliklar Irrasional tengsizliklar
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Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m 27 3. î í ì ¹ ³ Û ³ 0 ) ( 0 ) ( ) ( 0 ) ( ) ( x Q x Q x P x Q x P . 4.
î í ì ¹ £ Û £ . 0 ) ( 0 ) ( ) ( 0 ) ( ) ( x Q x Q x P x Q x P .
Moduli tenglamalar quyidagicha ekvivalent almashtirish bilan yechiladi: 1. ( )
( ) ( )
0 f x f x f x = Û ³ ; 2. ( )
( ) ( )
0 f x f x f x = -
Û £ ; 3. ( )
( ), ( )
0, ( )
( ) ( )
( ), ( )
0; F x f x agar F x F x f x F x f x agar F x = > é = Û ê = - < ë 4. 2 2 ( ) ( ) ( )
( ) f x g x f x g x = Û = ; 5.
2 2 ( ) ( 0) ( ) f x a a f x a = > Û = ; 6. ( ,
) 0,
0, ( ,
) 0 ( , ) 0, 0; F x x a agar x a F x x a F x x a agar x a - = - ³ é - = Û ê - +
= - <
ë 7. ( ) ( ), ( )
( ) ( )
( ); f x g x f x g x f x g x = é = Û ê
= - ë 8. ( ) ( ), 0, ( ) ( ) ( ) ( ), 0; f x g x agar x f x g x f x g x agar x = ³ é = Û ê - = < ë 9. ( ) ( )
( 0) ( ) f x a f x a a f x a = é = > Û ê = - ë ; 10. ( ) ( 0) f x a a =
Û Æ .
Moduli tengsizliklar quyidagicha ekvivalent almashtirish bilan yechiladi: 1. ( )
( 0) ( ) f x a a a f x a < > Û- <
< ; 2. 2 2 ( )
( 0) ( ) f x a a f x a > > Û > yoki
( ) , ( ) ( 0)
0 ; ( ) ; f x a f x a a agar a x R f x a > é > > Û
< Þ Î ê
ë 3.
2 ( )
( ) ( )
( ) f x x f x x j j < Û
; 4.
( ) ( ) ( ) ( ), 0; f x g x agar x f x g x f x g x agar x < ³ é < Û ê
- < < ë 5. ( ) ( ),
( ) ( )
( ) 0 ; ( ) ( );
f x g x f x g x agar g x x f x g x < ì
Û £ Þ ÎÆ
í- < î
A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m 28 6. ( ) ( ), ( ) ( ) 0, ( )
( ) ( )
( ) ( ) ( ) 0; f x g x f x g x agar x f x g x yoki f x g x f x g x agar x é > é > ³ > Û ê
ê < - - > < ê ê ë ë 7. ( ) ( )
2 2 ( ) ( ) 0 0
( ) 0 0 ; 0, n n n a f x b f x c f x y ay by c y n N + + ³ £ Þ = Þ + + ³ £
³ Î
Irrasional tenglamalarni umumiy holda quyidagicha ekvivalent almashtirish yordamida yechish mumkin ( )
N Î : 1. 2 2 ( ) 0, ( ) ( ) ( )
0, ( )
( ). n n f x f x x x f x x j j j ³ ì ï = Û ³ í ï = î 2. 2 2 ( ) 0, ( )
( ) ( )
0, ( )
( ). n n f x f x x x f x x j j j ì ³ ï = Û ³ í ï = î 3. 2 ( )
( 0) . n f x a a x =
4. 2
2 1 ( ) ( ) ( )
( ) n n f x x f x x j j + + = Û = . 5. 2 1 2 1
( ) ( )
( ) ( )
n n f x x f x x j j + + = Û = . 6. ( ) 2 ( )
0, ( 0), ( ) 0, ( ) ( ) ( )
( ) .
a x f x x a f x a x j j j ³ ³ ³ ìï - = Û í = + ïî 7. ( ) 2 ( ) 0, ( ) 0, ( ) 0, ( )
( ) ( 0) ( ) ( )
. f x x b x f x x b b f x b x j j j j ì ³ ³ - ³ ï + = ³ Û í = - ïî Irrasional tengsizliklar Irrasional tengsizliklar quyidagicha ekvivalent almashtirish yordamida yechiladi ( )
N Î : 1. 2 2 ( ) 0, ( ) ( ) ( )
0, ( )
( ). n n f x f x g x g x f x g x ì ³ ï < Û > í ï
î 2.
2 2 ( ) 0, ( )
( ) ( )
0, ( )
( ). n n f x f x g x g x f x g x ³ ì ï < Û ³ í ï
î 3.
2 1 ( )
( ) ( )
( ). n n f x g x f x g x + + < Û
4. 2 1
2 1 ( )
( ) ( )
( ). n n f x g x f x g x + + < Û
5. 2
( ) 0, ( ) 0,
( ) ( )
( ) 0, ( )
( ). n n g x f x f x g x g x f x g x é
ì í
³ î ê > Ûê ³ ìï êí ê > ïî ë 6. 2 1
2 1 ( )
( ) ( )
( ). n n f x g x f x g x + + > Û > Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m 29 7. 2 2 2 ( ) 0, ( )
0, ( )
1 ( )
0, ( )
( ) ( ).
( ) ( )
n n n g x g x f x f x g x f x g x f x g x ì
> ì
ï > Û
³ í í > ïî ï < î U 8. 2 2 ( ) 0, ( ) 0, ( )
0, ( )
1 ( )
0 ( )
( ) ( ).
n n g x f x g x f x f x g x f x g x > ³ ì < ì ï < Û í í ³ < ï î î U
1.
- hadini topish formulasi: ( ) 1 1 , ,
n a a n d n N = + -
Î d - ayirmasi, 1
- birinchi hadi, n a n-chi hadi, n - hadlari soni. 2. d - ayirmani toppish: 2 1
2 4 3 1 ...
n n d a a a a a a a a - = - = - = - = = - yoki ( ) ( )
m d a a n m = - - . 3. Xossalari: a) 1 1 2 k k k a a a - + + = yoki 2 n k n k n a a a - + + = { } n a ketma-ketlik arifmetik progressiya bo’ladi; b) (
; ; n m n m k p a a n m d a a a a n m k p - = - + = + « + = +
v) 1 2 1 3 2 1 ...
; n n n n k k a a a a a a a a - - - + + = + = + = =
+ 4. Dastlabki n ta hadi yig’indisi - n S : 1) 1 2 3 ... ;
n S a a a a = +
+ + + 2)
1 ;
n n S S a - - = 3)
1 1 ( ) 2 ( 1) ; 2 2 n n n a a n a d n S S n + + - = = × ; ( 1) 2 n n S n a + = × ; 4)
n k n k S S S n k d + = + + × ×
; 5) ( ) , m n m n m n S S S m n m n + + = - ¹ - ; 6) ( 1),
k n n S S d n k = + × × - k n S -
gacha bo`lgan sonlar yig; 7)
2 4 2 1 3 2 1 ...
... n n a a a a a a n d - + + + = + + + + × ; Geometrik progressiya 1.
- hadini topish formulasi: 1 1 ,
, n n b b q n N - = Î bu yerda q -maxraji, 1
- birinchi hadi, n b n-chi hadi, n - hadlari soni. Click here to buy A B B Y Y PD F Transfo rm er 2 .0 w w w .A B B Y Y. c o m Download 0.8 Mb. Do'stlaringiz bilan baham: 
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