|
(222
—
224):
222.
1)
a
va
b
sonlar ko‘paytmasining ikkilangani;
2)
b
va
c
sonlar ko‘paytmasining uchlangani;
3)
x
va
y
sonlar kvadratlarining ko‘paytmasi;
4)
a
son bilan
b
son kvadratining ko‘paytmasi.
223.
1)
m
sonning kubi bilan
p
sonning ko‘paytmasi;
2)
a
sonning kvadrati bilan
b
son ko‘paytmasining uch-
langani.
224.
1)
t
soatdagi sekundlar soni;
2)
n
metrdagi santimetrlar soni.
M a s h q l a r
71
225.
1) Berilgan o‘lchamlar bo‘yicha
shtrixlangan yuzni hisoblash formu-
lasini chiqaring (9- rasm);
2) 2
bc
+ 2
c
(
a
-
2
c
) = 2
ac
+ 2
c
(
b
-
2
c
)
tenglikning to‘g‘riligini shakl yorda-
mida ko‘rsating;
3) Shtrixlangan yuzni ikkita to‘g‘ri
to‘rtburchak yuzlarining ayirmasi si-
fatida tasvirlang. Bundan foydalanib,
ab
-
(
b
-
2
c
)(
a
-
2
c
) = 2
ac
+ 2
c
· (
b
-
2
c
) tenglikni isbotlang.
226.
Birhadning son qiymatini toping:
1)
= -
, bunda
;
a
a
3
3
4
2
2)
2
0,5
4
b
b
= -
, bunda
;
3)
=
=
=
, bunda
,
;
a
c
abc
, b
1
1
2
3
3
2
4)
=
=
=
, bunda
,
;
pqr
p
q
, r
1
1
2
6
4
3
5)
-
=
= -
, bunda
;
m
n
m
n
2
1
7
( 0,2)
3,
35
6)
-
= -
=
, bunda
y
x
y
x
2
1
9
( 0,3)
15,
6.
227.
Birhadni standart shaklda yozing:
1)
m m
2
3
;
3)
0,5;
ab
5)
( )
-
pq
pq
2
2
5
4
;
2)
z z z
5
5
;
4)
( ) (
)
-
-
m
m
3
;
6)
( )
-
qp
pq.
2
3
2
2
3
228.
Birhadni standart shaklda yozing va son qiymatini toping:
1)
= -
=
, bunda
;
a
ac c
, c
1
3
12
4
2)
= -
=
, bunda
;
a b
ba
a
b
2
3
1
3
1
4
2
6
8
2,
229.
(Qadimiy masala.)
Hovuzga 4 ta quvur o‘tkazilgan bo‘lib,
birinchi quvur hovuzni bir kunda, ikkinchi quvur ikki
kunda, uchinchi quvur uch kunda, to‘rtinchi quvur
to‘rt kunda to‘ldiradi. To‘rtala quvur birgalikda hovuzni
qancha vaqtda to‘ldiradi?
c
c
c
a
¾¾
®
b
9- rasm.
72
Birhadlarni ko‘paytirish
Quyidagi masalani yechaylik.
Masala.
To‘g‘ri burchakli parallelepiðedning hajmi
V
=
abc
formula bo‘yicha hisoblanadi, bu yerda
a
— parallelepiðedning
bo‘yi,
b
— eni va
c
— balandligi. Agar shu parallelepiðedning
bo‘yi 5 marta, eni 2
n
marta, balandligi 3
n
marta uzaytirilsa,
yangi parallelepiðedning hajmi qanday bo‘ladi?
Yangi parallelepiðedning o‘lchamlarini topamiz: bo‘yi
5
a
, eni 2
nb
, balandligi 3
nc
. Bu holda uning hajmi
V
1
=(5
a
)·(2
nb
)·(3
nc
)
bo‘ladi.
(5
a
)·(2
nb
)·(3
nc
) ifoda quyidagi uchta birhadning ko‘payt-
masidir: 5
a
, 2
nb
, 3
nc
. Sonlarni ko‘paytirish qoidalariga ko‘ra
bunday tenglikni yozish mumkin:
(5
a
)·(2
nb
)·(3
nc
) = 5
a
· 2
nb
· 3
nc
= (5·2·3)(
annbc
) = 30
n
2
abc
.
Birhadlarni ko‘paytirish natijasida yana birhad hosil bo‘ladi
va uni standart shaklda yozib, soddalashtirish lozim, masalan,
(3
a
2
b
3
c
)·(4
ab
2
) = 3
a
2
b
3
c
·4
ab
2
= 12
a
3
b
5
c
.
(3
a
2
b
3
c
) · (4
a b
2
) = 12
a
3
b
5
c
.
Ikki yoki bir nechta bir xil birhadlarning ko‘paytmasini,
ya’ni birhadning darajasini qaraymiz, masalan, (5
a
3
b
2
c
)
2
. Bu
birhad 5,
a
3
b
2
c
ko‘paytuvchilarning ko‘paytmasi bo‘lgani
uchun ko‘paytmani darajaga ko‘tarish xossasiga ko‘ra:
(5
a
3
b
2
c
)
2
= 5
2
(
a
3
)
2
(
b
2
)
2
c
2
= 25
a
6
b
4
c
2
.
Xuddi shu kabi:
(2
pq
2
)
3
= 2
3
p
3
(
q
2
)
3
= 8
p
3
q
6
.
Birhadni natural ko‘rsatkichli darajaga ko‘tarish natijasida
yana birhad hosil bo‘ladi.
12-
73
Birhadlarni ko‘paytiring
(230—237):
230.
1)
( ) ( )
2
3 ;
a
b
2)
( ) ( )
3
2 ;
a
b
3)
(
)
2
3
3
;
b
b
-
4)
(
)
-
a a
2
2
;
231.
1)
( )
(
)
2
2
3
;
p
c
-
3)
( ) ( )
2
3
4
6
;
a
a
2)
(
)
2
5
7 ;
m
n
-
-
4)
( )
-
b
b
3
2
1
2
8
.
232.
1)
a
b
3
2
1
4
0,3
;
3)
(
)
(
)
2
0,2
1,3
;
p
q
-
2)
(
)
3
8
0,25 ;
m
n
-
4)
-
-
c
b
2
3
3
5
7
6
.
233.
1)
(
)
-
ab
a b
2
3
2
;
3)
ab
ac
2
2
1
4
8
;
2)
(
) (
)
2
2
4
7
;
x y
xy
-
-
4)
(
)
a b
bc
2
2
1
3
6
.
234.
1)
(
) (
)
2 5
3
2
3
6
;
a b c
a bc
3)
a b x
a bx
2 3
3
2
2
3
3
4
;
2)
(
) (
)
5 2
4
7
3
;
a b c
ab c
-
4)
-
3
3
2
3
3
2
4
;
a
a
xy
y
235.
1)
(
)
5 6 2
3
0,4
1,2
;
x y z
xyz
-
-
3)
-
-
x y
xy
z
z
2 3
2 3
1
1
3
2
1
1
;
2)
(
) (
)
4
5 2
2 5
2,5
3
;
n m r
nm r
-
4)
-
a b c
a b c
2 5 3
3 2 4
1
1
4
3
2
3
.
236.
1)
(
) (
)
-
-
m
n
mn
2
1
3
24
4
;
2)
(
)
(
)
-
-
-
n
m
mn
2
1
6
;
18
5
3)
(
)
ay
x y
a x
3
2
3
1
3
3
4
0,2
;
4)
(
)(
)(
)
-
-
-
a bc
ab c
abc
2
2
3
.
13
5
0,4
237.
1)
( )
( )
2
2
3
4
5
;
a
b
a b
ab
-
3)
(
)
(
) (
)
-
ab
bc
ac
ab
1
4
1,5
2
24
;
2)
( )
(
) (
)
2 2
5
2
3 ;
a a b
b
a
-
-
4)
(
)
-
-
a
ab
bc
c
2
2
1
3
.
1,2
5
2
M a s h q l a r
74
Birhadni darajaga ko‘taring
(238—241):
238.
1)
3
(2 ) ;
a
2)
2
(5 ) ;
b
3)
4
(3 ) ;
b
2
4)
2
(2 ) .
a
3
239.
1)
4
( 3 ) ;
-
ab
2)
2
( 4 ) ;
-
ab
3)
5
(
) ;
-
abc
4)
3
( 2
) .
-
xyz
240.
1)
3
( 2
) ;
-
a b
2
2)
5
(
) ;
-
a bc
2
3)
2
( 3
) ;
-
x y
3
4)
3 4
( 2
) .
õ
-
y
2
241.
1)
3
1
2
;
nm
2
2)
4
2
1
3
;
n m
2
3)
3 3
( 0,1
) ;
-
a b
3
4)
3
a b
2 2
(0,4
) .
Amallarni bajaring
(242—243):
242.
1)
(
)
3
( 2 )
3 ;
-
-
a
a
3)
(
)
2
2
( 0,2
) 20
;
-
bc
cx
2
2)
( )
3
( ) 2 ;
-
a
a
4)
(
)
2
2
( 0,1
) 100
.
-
ab c
by
2
243.
1)
-
-
3
2
2
3
1
5
2
1
;
x y
c x
3
2
3)
(
)
2
3
2
( 3
) 2
;
-
bc
ab
2
2)
2
3
1
4
2
;
y
2
x
xy
2
3
4)
(
)
3
2
3
( 2
)
.
-
-
2
a b
a b
2
244.
Birhadni boshqa birhadning kvadrati shaklida yozing:
1) 9
a
2
;
2) 16
x
4
;
3) 25
a
2
b
4
;
4) 81
x
6
y
2
; 5) 36
x
10
y
4
;
6) 1,21
a
8
b
4
.
245.
Birhadlarni ko‘paytiring va hosil bo‘lgan ifodaning qiy-
matini toping:
1)
×
= -
=
a
a b
a
b
2
2
1
5
3
7
bunda
3
,
2,
;
2)
×
=
=
mn
n
m
n
2
2
5
10 , bunda
0,8,
4;
3)
×
=
=
=
2
a
a b c
a
b
c
2
1
1
16
4
bunda
4
,
4,
;
3;
4)
×
=
= -
=
2
0,7
100 , bunda
0,3,
0,2,
4.
m n
np
m
n
p
246.
(Qadimiy masala.)
Baliqning uchdan bir qismi loyda,
to‘rtdan bir qismi suv tagida va uch qarichi suv ustida.
Baliqning uzunligi necha qarich?
Do'stlaringiz bilan baham: |
