Ko‘rsatkichli tenglama va tengsizliklar
![Mavzu: Ko‘rsatkichli tenglama
va tengsizliklar](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_1.png)
![Noma’lum daraja ko‘rsatkichida
ishtirok etadigan tenglamalarga
ko‘rsatkichli tenglamalar deyiladi.
Sodda ko‘rsatkichli tenglama
quyidagi ko‘rinishga ega:
bunda](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_2.png)
![yechimga ega. yechimga ega
emas.
yechimga ega. yechimga ega
emas.](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_3.png)
![x1-misol. Tenglamaning yeching:??????
???????????? ?????? + ??????
= ??????
???????????? − ??????
???????????? ?????? + ?????? = ???????????? − ??????
???????????? ?????? + ?????? = ???????????? − ??????
?????? =
????????????
????????????
=
??????
??????
= ??????
??????
??????
???????????? ?????? = ????????????
Javob: bo‘lsa ,](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_4.png)
![Yechish usullari:
Bir xil asosga keltirish usuli;
Umumiy ko‘paytuvchini qavsdan tashqariga
chiqarish usuli;
Yangi o‘zgaruvchi kiritish usuli;
Hadma-had bo‘lish usuli;
Grafik usul.](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_5.png)
![Bir xil asosga keltirish usuli??????
?????? + ??????
= ????????????
??????
??????
?????? + ??????
= ??????
?????? ??????
?????? + ?????? = ?????? ??????
?????? = ?????? ?????? − ??????
?????? = ??????
Javob: 72-misol.](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_6.png)
![Umumiy ko‘paytuvchini qavsdan tashqariga
chiqarish usuli??????
?????? + ??????
+ ??????
??????
= ??????
??????
??????
∙ ??????
??????
+ ??????
??????
= ??????
??????
??????
∙ ( ?????? + ?????? )= ??????
??????
??????
∙ ?????? = ?????? ??????
??????
= ??????
??????
??????
= ??????
??????
?????? = ??????
Javob: 03-misol.](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_7.png)
![Yangi o‘zgaruvchi kiritish usuli??????
??????
− ?????? ∙ ??????
??????
− ???????????? = ??????
??????
??????
= ??????
??????
??????
− ?????? ?????? − ???????????? = ??????
??????
??????
= ?????? ??????
??????
= − ??????
??????
??????
= ??????
??????
??????
= ??????
??????
?????? = ??????
??????
??????
= − ??????
?????? ?????? ∅
Javob: 24-misol.](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_8.png)
![Hadma-had bo‘lish usuli;?????? ∙ ????????????
??????
+ ?????? ∙ ????????????
??????
− ???????????? ∙ ??????
??????
= ??????
?????? ∙ ??????
?????? ??????
+ ?????? ∙ ??????
??????
∙ ??????
??????
− ???????????? ∙ ??????
?????? ??????
= ?????? : ??????
?????? ??????
?????? ∙
(
??????
??????
)
?????? ??????
+ ?????? ∙
(
??????
??????
)
??????
− ???????????? = ??????
(
??????
??????
)
??????
= ??????
?????? ??????
??????
+ ?????? ?????? − ???????????? = ??????
??????
??????
= ?????? ?????? ?????? = −
????????????
??????
5-misol.](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_9.png)
![(
??????
??????
)
??????
= ??????
(
??????
??????
)
??????
=
(
??????
??????
)
??????
?????? = ??????
(
??????
??????
)
??????
= −
????????????
??????
?????? ?????? ∅Javob: 0](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_10.png)
![Grafik usuli
tenglamani yechamiz.
Bitta koordinata
tekisligida
va
funksiyalarning
grafigi yasaladi.?????? − ????????????
??????
− ??????
?????? = ??????
??????
?????? = ?????? − ??????
??????
??????](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_11.png)
![Grafiklar
kesishgan
nuqtaning
abssissasi
berilgan
tenglamani
ildizi
bo‘ladi. ?????? − ????????????
??????
− ??????
?????? = ??????
??????
?????? = ?????? − ??????
??????
??????](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_12.png)
![Daraja ko ‘rsatkichida noma’lum
ishtirok etadigan tengsizliklarga
ko‘rsatkichli tengsizliklar deyiladi.
Ko‘rsatkichli tengsizliklar umumiy
ko‘rinishlari:
,
,
,
,](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_13.png)
![, tengsizlik:
bo‘lganda
tengsizlikka teng kuchlidir.
bo‘lganda
tengsizlikka teng kuchlidir.](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_14.png)
![](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_15.png)
![6-misol. ( ?????? , ?????? )
??????
<
??????
???????????? Tengsizlikni yeching:
(
??????
??????
)
??????
<
(
??????
??????
)
??????
?????? <
??????
??????
< ??????
?????? > ??????
??????
Javob:](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_16.png)
![??????
?????? ?????? − ??????
≤ ????????????
?????? − ?????? ??????
??????
?????? ?????? − ??????
≤ ( ??????
??????
)
?????? − ?????? ??????
???????????? = ??????
??????
??????
?????? ?????? − ??????
≤ ??????
?????? − ?????? ??????
?????? ?????? − ?????? ≤ ?????? − ?????? ??????
?????? ?????? + ?????? ?????? ≤ ?????? + ??????
???????????? ?????? ≤ ????????????
?????? > ??????
?????? ≤ ??????
??????Javob:
→
→7-misol. Tengsizlikni yeching:](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_17.png)
![??????
?????? + ??????
− ??????
??????
≥ ??????????????????
??????
??????
∙ ?????? − ??????
??????
≥ ??????????????????
??????
??????
∙ ( ?????? − ?????? ) ≥ ??????????????????
??????
??????
∙ ?????? ≥ ??????????????????
??????
??????
≥ ?????????????????? : ??????
??????
??????
≥ ??????
??????
?????? > ?????? →
?????? ≥ ??????
??????Javob :
??????
??????
≥ ????????????8-misol. Tengsizlikni yeching:](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_18.png)
![??????
?????? + ??????
> ??????
?????? + ??????
: ??????
?????? + ??????
??????
?????? + ??????
??????
?????? + ??????
> ??????
(
??????
?????? )
?????? + ??????
>
(
??????
?????? )
??????
??????
??????
< ??????
?????? < − ??????
?????? + ?????? < ??????
→
?????? =
(
??????
??????
)
??????
→
− ??????Javob: 9-misol. Tengsizlikni yeching:](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_19.png)
![Topshiriq
Darslikning 99-100-sahifalarida
berilgan 19- va 26-misollarni yeching.](/data/documents/54f9796b-fc62-4bf7-bc11-09ada0e2d3a2/page_20.png)
Mavzu: Ko‘rsatkichli tenglama va tengsizliklar
Noma’lum daraja ko‘rsatkichida ishtirok etadigan tenglamalarga ko‘rsatkichli tenglamalar deyiladi. Sodda ko‘rsatkichli tenglama quyidagi ko‘rinishga ega: bunda
yechimga ega. yechimga ega emas. yechimga ega. yechimga ega emas.
x1-misol. Tenglamaning yeching:?????? ???????????? ?????? + ?????? = ?????? ???????????? − ?????? ???????????? ?????? + ?????? = ???????????? − ?????? ???????????? ?????? + ?????? = ???????????? − ?????? ?????? = ???????????? ???????????? = ?????? ?????? = ?????? ?????? ?????? ???????????? ?????? = ???????????? Javob: bo‘lsa ,
Yechish usullari: Bir xil asosga keltirish usuli; Umumiy ko‘paytuvchini qavsdan tashqariga chiqarish usuli; Yangi o‘zgaruvchi kiritish usuli; Hadma-had bo‘lish usuli; Grafik usul.