479
Isbot:
Faraz qilaylik bu son 169 ga bo’linsin.U holda
0
169
16
5
169
16
5
2
2
k
x
x
k
x
x
farazimizga binoan
k
D
169
16
4
25
D
natural son.
13
3
13
13
4
39
169
4
169
16
4
25
k
k
k
D
korinib
turibdi
D
to’la kvadrat son 13 ga bo’linadi ammo
2
13
ga bo’linmaydi.
2.
61
3
3
xy
y
x
tenglamani natural sonlarda yeching.
Yechim:
y
x
,
natural son bo’lgani uchun
61
xy
ham natural son bo’ldi,u holda
3
3
y
x
natural son bo’lishi uchun x>y bo’lishi kerak.U holda
n
x
y
desak,bunda
n
natural son bo’lishi kerak.Bundan
0
61
3
1
3
61
3
2
2
3
3
n
x
n
n
x
n
n
x
x
n
x
x
tenglamani
x
ga
nisbatan yechamiz.Yechimga ega bo’lishi uchun
0
61
3
n
bo’lishi kerak.Demak,
3
,
2
,
1
n
larni x ga nisbatan kvadrat tenglamalarni yechamiz.Bunda
faqat
1
n
da
0
60
2
2
2
x
x
tenglamani yechib
5
,
6
y
x
javoblarini olamiz.
3
.(Samandarov.B)
c
b
a
,
,
kamayuvchi o’tkir burchakli uchburchakning tomonlari
bo’lsa
3
2
)
2
2
2
2
c
a
a
c
b
b
a
tengsizlikni isbotlang.
Avval bir lemmani kvadrat tenglamadan foydalanib isbotlaymiz.
Lemma:
Tomonlari
c
b
a
,
,
bo’lga o’tkir burchakli uchburchakda
c
ni qarshisida
burchak yotsa
,
sin
a
c
va
b
c
sin
tengsizliklar o’rinli.
Isbot:
kosinuslar teoremasidan
)
1
(
0
cos
2
0
cos
2
2
2
2
2
2
2
c
b
a
b
a
c
ab
b
a
(1) ni
a
ga nisbatan kvadrat tenglama qilib olsak.Bu tenglama masala shartida
doimo yechimga ega bo’lgani uchun
b
c
c
b
b
sin
0
4
cos
4
2
2
2
2
2
2
2
2
2
2
2
1
1
sin
1
1
cos
1
cos
sin
c
b
b
c
b
c
b
c
b
c
b
c
b
c
tg
xuddi
Shunday
2
2
c
a
a
tg
3
2
2
2
2
2
2
tg
c
a
a
c
b
b
3
2
2
tg
tengsizlikni isbotlash qiyin emas chunki max{
}=60
4.(XMO-2003,Yaponiya)Natural a,b sonlarning
1
2
3
2
2
b
ab
a
kasr
natural
qiymatlarni qabul qiladigan barcha (a,b) juftliklarni toping.
Yechim:
a,b natural sonlar uchun
0
1
2
3
2
2
b
ab
a
k
bo’lgani uchun
0
1
2
3
2
b
ab
bundan
2
2
2
1
b
ab
yani
2
/
b
a
kelib chiqadi.
1
k
dan
1
2
1
2
2
3
2
2
b
a
b
b
ab
a
ga ega bo’lamiz.Bu esa
2
2
2
2
2
2
sin
sin
sin
1
)
c
b
a
c
b
480
1
2
2
2
b
a
b
a
Tengsizlikni olib keladi.Demak quyidagi shart bajariladi.
b
a
yoki
b
a
2
(1)
Endi
a
ga nisbatan biz
0
1
2
3
2
2
b
k
a
kb
a
(2)
Tenglamaning
1
a
va
2
a
ildizlarini qaraymiz va ulardan bittasi butun son
bo’lishini faraz qilamiz.Viyet teoremasiga ko’ra
2
2
1
2
kb
a
a
bo’ladi.yani
ikkinchidan ildizi ham butun son bo’lishi shart.Bundan tashqari
1
3
2
1
b
k
a
a
tengliklardan quyidagiga ega bo’lamiz.
b
kb
b
k
a
b
k
a
2
3
1
3
2
1
1
0
(1) ni hisobga olsak
0
2
a
holda ,
1
3
b
yani
2
/
2
b
a
(b juft son bo’lganda)
hosil qilamiz.
0
2
a
holda
0
1
3
b
yani
1
,
2
1
b
k
a
bo’ladi.
2
/
2
b
a
holda
4
/
4
b
k
va
2
/
4
/
4
1
b
b
a
bo’ladi.
Demak talab qilinayotgan (a,b) juftlik faqat quyidagilardan bittasi bo’lishi
mumkin.
(a,b)=(2s,1), yoki (a,b)=(s,2s),yoki (a,b)=( 8
s
s
s
2
,
4
).
5.
a
a
x
x
a
x
x
16
cos
26
)
6
(
10
)
6
(
2
2
2
tenglama ikkita ildizga ega
bo’ladigan
a
parametrning barcha qiymatlarini toping.
Yechim:
a
x
x
z
6
2
belgilash kiritib, berilgan
tenglamani quyidagi
ko’rinishga keltiramiz:
1
16
cos
)
5
(
16
cos
26
10
2
2
a
z
a
z
z
.
Oxirgi tenglamaning chap tomoni doimo manfiymas , o’ng tomoni esa doimo
musbatmas . Bu yerdan ularning ikkalasi ham nolga tengligi, ya’ni ushbu tenglamalar
sistemasi o’rinli ekanligi kelib chiqadi:
.
8
,
4
,
2
,
1
0
5
6
1
)
/
16
cos(
0
5
6
0
1
)
/
16
cos(
0
5
6
5
2
2
2
a
a
x
x
a
a
x
x
a
a
x
x
z
.
Berilgan tenglama ikkita ildizga ega bo’lishi uchun yuqoridagi sistemaning
birinchi
t
2
−6
t+a+
5=0 (
x
t
) tenglamasining bitta ildizi musbat, ikkinchi ildizi esa
manfiy yoki ikkala ildizi teng va musbat bo’lishi kerak.
Birinchi holda,
Viet teoremasiga asosan, ildizlar ko’paytmasiga teng bo’lgan
a
+5<0, ya’ni
a
< −5 bo’lishi kerak. Bu holda, sistemaning ikkinchi tenglamasi
javoblaridan,
a
= − 8 ekanligi kelib chiqadi.
Ikkinchi holda kvadrat tenglamaning diskriminanti nolga teng, ya’ni uning chap
tomoni aniq kvadrat bo’lishi kerak. Bu esa faqat
a
=4 holda bajariladi.
Demak, berilgan tenglama
a
=4 yoki
a
= −8 bo’lganda ikkita ildizga ega bo’ladi.
482
Because it is important to reach a conversational level
of comprehension of the
language so that we can understand what is being said to us. That means in order to
converse properly we need to prepare ourselves for a long time. Being shy is the one
which I always encounter. In order to succeed in losing timidity, make a little
conversation with yourself, using common phrases. A shining example might be in the
following:
-
Hi, how are you?
-
Hi, good, thanks. And you?
-
Fine. Thanks a lot.
And so on… Then build up these functional phrases and repeat them until you
can handle the situation with confidence. And sometimes when you meet new people,
you do not know what to say. The more you learn about cultures and customs, the more
you able to communicate with them. This will open your eyes to see new backgrounds.
And you will expand your understanding of different people and appearing questions.
[1] The
advantages
to learning English while travelling include:
-You cannot escape the language. Because when you are learning English to
travel, your main goal will be communication. No matter how
many grammar rules
you know or how much vocabulary you understand. If you want to speak to foreigners,
you have to speak.
- You have a chance to enjoy the profits of learning more, since you are able to
communicate better with the people around you. This is a fantastic motivation.
- You can meet new people, with some of them being fellow travelers and
students trying to learn English like you. And this is a favorable way to learn together.
- The most obvious one is learning English while travelling cannot take a lot of
time and it provides plenty of motivation. This is especially true for mastering a
language properly. Because keeping up the motivation can sometimes be difficult on
learning by textbook if progress is slow.
- The last one
is you will learn English, also you will be in a highly
advantageous position at the same time. This is more enjoyable. [2]
And in learning English while travelling, you only enjoy from the benefits
mentioned above. There is no doubt that travel is the only thing you buy, that makes
you richer. To travel is to discover that everyone is wrong about other countries. Not
to worry, if you practice the right way, it will not feel like study at all. If you do not
understand the responses at first, that is no real problem. Just get started. Now you are
learning and speaking another language. At this time, you should know some phrases
such as greetings that you say at the beginning of a communication. They are essential
to conversation, while you are travelling in order to learn and improve your English.
Because as you know, English can be very important to communicating the right details
in an international and also national travel situation.
If you want to be fluent in English, you need to surround yourself with English.
Luckily English is all over the world. You can travel almost anywhere and have a
chance to practice your English. [3]
483
As you see, for media, international politics and business, English is estimated
that it is the most widely-spoken language overall.
Taking these
points into consideration, I emphasize that travel makes you
storyteller. So my purpose in this article is to inspire young generation to go to
sightseeing to improve their language skills and influence on their experience. I can
say without any doubt that depending on my experience in Samarkand and Bukhara,
travel is only way to learn easily and quickly.
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