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Qisqa kо`рaytirish fоrmulalari va ularning
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- Ayrim qisqa kо`рaytirish fоrmulalari
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- Murakkab ildiz formulasi
- Qisqa kо`рaytirish fоrmulalarni ildizli ifоdalarga qо`llanishi
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Qisqa kо`рaytirish fоrmulalari va ularning umumlashmalari 1. 2 2 2 ( ) 2
b a ab b + = + + . 2. 2 2 2 ( ) 2 a b a ab b - = - + . 3. 2 2 ( )( ) a b a b a b - = -
+ . 4. 3 3 2 2 3 ( ) 3 3 .
b a a b ab b + = + + + 5. 3 3 2 2 3 ( ) 3 3 .
a a b ab b - = - + - 6. 3 3 2 2 ( )( ) a b a b a ab b - = - + + . 7. 3 3 2 2 ( )( ) a b a b a ab b + = +
- + . 8. Ayrim qisqa kо`рaytirish fоrmulalari: 1)
4 4 2 2 3 2 2 3 ( )( )( ) ( )( ) a b a b a b a b a b a a b ab b - = - + + = - + + + ; 2) 5 5 4 3 2 2 3 4 ( )( ) a b a b a a b a b ab b - = - + + + + ; 3) 5 5 4 3 2 2 3 4 ( )( ) a b a b a a b a b ab b + = + - + - + ; 4) ( )( ) ( ) ( ) ( ) ( ) ( ) 6 6 3 3 3 3 2 2 2 2 2 2 a b a b a b a b a ab b a b a ab b a b - =
- + = - + + + - + = - ´
( )( ) 2 2 2 2 a ab b a ab b ´ + + - + = ( ) ( ) 5 4 3 2
2 3 4 5 a b a a b a b a b ab a - + + + + + ; 5) ( )
ac ab c b a c b a 2 2 2 2 2 2 2 + + + + + = + + ; 6) ( )
ac ab c b a c b a 2 2 2 2 2 2 2 + - - + + = - - ; 7) ( ) + + + + + + + + = + + +
ad ac ab d c b a d c b a 2 2 2 2 2 2 2 2 2 2 2 bd cd + ; 8) ( ) - - - - + + + + = - - + bc ad ac ab d c b a d c b a 2 2 2 2 2 2 2 2 2 2 2 bd cd + ; 9) ( ) ( ) ( ) (
) ( ) ( ) 2 2 2 2 2 4 3 3 ; m n m n m n m m n n m n m n a b a b a b a a b b a b a b + × - × - × + + = - × - 10)
( ) 1 2 2 1 ( 1) ! ... ... 2 !( )! n n n n n k k n n n n n a b a na b a b a b nab b k n k - - - - - + = +
+ + +
+ + + - ; 11)
( ) (
) ( ) ( )( )( ) 3 3 3 3 a b b c c a a b b c c a - + - + - = - - - . Ba’zi yig’indilar ( ) ( 1) 1. 1 2 3 4 ; 2. 2 4 6 8 2 1 ; 2 n n n n n n + + + + +×××+ = + + + +×××+ = + 2 3. 1 3 5 7 2 1
n n + + + +×××+ - = 2
2 ( 1)(2 1) 4. 1
2 ...
; 2
n n + + + + + = 2 2 2 1 1 1 1 5. 1 1 ...
1 , (
2) 2 3 2 n n n n + æ ö æ ö æ ö - + - + + - = ³ ç ÷ ç
÷ ç ÷ è ø è
ø è ø ; 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 14 1 1 1 6. 1
... 2 2 4 8 + + + + = ; 1 1 1 1 7. ... ; 1 2 2 3 3 4 ( 1)
n n n n + + + + = × × × + + 2 2 3 3 3 3 ( 1) 8. 1 2 3 ... 4
n + + + + + = 1 1 1 1 9. ...
; 1 3 3 5 5 7 (2 1)(2
1) 2 1 n n n n + + + + = × × × - + + ( ) ( ) 3 3 3 3 3 2 2 10. 1
3 5 7 ... 2 1 2 1 ;
n n n + + + + +
- = - 2 2 2 2 2 2 (4 1) 11. 1 3 5 7 ... (2 1) 3 n n n - + + + + + - = ; 2 1 12. 1 2 2 ... 2 2 1 n n - + + + + = - ( ) ( ) 2 13. 1 2 2 5 3 8 ... 3 1 1 ; n n n n × + × + × + + - = +
2 2 1 2 1 ( 1) 14. 1 2 3 4
( 1) 2
n n n n - - + - + - + + -
= - ; ( 1) ( 1) 15. 1 2 2 3 ... ( 1) 3 n n n n n - + × + × + + - = . Murakkab ildiz formulasi 1. 2 2 2 2 2 2
a b c a a b c a b c + - - - + = + . 2. 2 2 2 2 2 2 a a b c a a b c a b c + - - - - = - . 3. ...
n k k n n k n x y x y x y × = × . 4. 1 1 ... k k k k k x x x x x - = . 5. 2 2 1 ... , 1, 2,... n n x x x x n - = = . 6. 1 4 1 ... , 0 2 m m m m m m ± +
+ ± ± ± ± =
> . 7. 1 : : : ...
k k k k k x x x x x + = . Ildizning xossalari , 2 , , , 2
. n n a n k k N a a n k k N ì = Î ï = í = + Î ïî 1.
2 ( ) a a - = . 2. , ,
0. a b a b a b × = × >
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 15 3.
2 , 0.
a b a b a = × > 4. 2 , 0.
a b a b a = -
× < 5.
6 6 5 2 5 3 a b a b × = × . 6. 2 4
a b a b × = × . 7. 0 n a = , agar 0
= bо`lsa. 8. 1 =
a , agar
1 =
bо`lsa. 9. Agar a a da 0 , 0 > = a a bо`lsa, u hоlda a
10. Agar a a da 0 , 0 < = a a bо`lsa, u hоlda a a ratsiоnal kо`rsatkichli daraja ma`nоga ega emas. 11.
0, 0, 0; , ,
, , ,
2 a b c m n p N m n p > > > Î ³ sonlar uchun: a)
m n m n a a = ; b) n n n a b a b × =
× ; v) n n n a a b b = ; g) n n n a b a b × = × ; d) n m n m a a × = ; e) ( )
m n m n a a = ; j) 2 2 n n a a = ; k) 2 1 2 1 n n a a + + - = - ; l)
n m m n a a × = ; m)
2 a a = ; n) n p n m p m a a × × = ; o)
; n m p p n p p m n a b c a b c × ×
× = p) n k n k n k a a a × + × = ; r) : n k k n n k a a a × - = . 12. Qisqa kо`рaytirish fоrmulalarni ildizli ifоdalarga qо`llanishi: 1) ( )( ), 0, 0;
b a b a b a b - =
- + ³ ³ 2) ( )( ), 0, 0;
- =
- - - - + -
£ £ 3) ( ) 2 , 0; a b a b a b - =
- - ³
4) ( ) 2 , 0; a b a b a b + = + + ³
5) ( )( ) ; , , 0 0 2 2 2 2 ³ ³ + - = - b a b a b a b a n n n n n n 6) 2 2
3 3 3 3 ( )( ) ; a b a b a ab b - =
- + + 7) ( ) 2 2 3 3 3 3 3 ( ) a b a b a ab b + =
+ - + ; 8) ( ) ( )
2 2 3 2 2 1 2 2 1
2 1 2 2 1; - = - × +
= - = - 9) = ÷
ö ç è æ - - + = ÷ ø ö ç è æ - - + 2 2 3 2 2 5 3 2 2 5 6 2 5 6 2 5 ( ) (
) 2 2 2 3 2 3 2 8. æ ö + - - = ç ÷ è ø Download 0.8 Mb. Do'stlaringiz bilan baham: 
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