Tenglamalarni taqribiy yechish
![Mavzu:
Tenglamalarni taqribiy yechish](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_1.png)
![Mustaqil bajarilgan topshiriqni tekshirish
Javob:42. Tenglamalar sistemasini yeching. ?????? ¿
{
??????
?????? + ?????? ??????
= ??????????????????
??????
?????? ??????+ ?????? ???????????? − ?????? ??????
= ?????? {
??????
?????? + ?????? ??????
= ??????
??????
??????
?????? ??????+ ?????? ???????????? − ?????? ??????
= ??????
??????
{
?????? + ?????? ?????? = ??????
??????
??????
+ ?????? ???????????? − ??????
??????
= ??????
(?????? − ?????? ?????? )
??????
+ ?????? ?????? ∙ (?????? − ?????? ?????? )− ??????
??????
= ??????
⟹ ?????? = ?????? − ?????? ??????
?????? − ???????????? ?????? + ?????? ??????
??????
+ ?????? ?????? − ?????? ??????
??????
− ??????
??????
= ??????
??????
??????
+ ?????? − ?????? = ?????? ?????? ?????? = − ?????? ; ?????? ?????? = ??????
?????? ?????? = ?????? ?????? ?????? = ??????](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_2.png)
![Mustaqil bajarilgan topshiriqni tekshirish
Javob:42. Tenglamalar sistemasini yeching. ?????? ¿
{
????????????
??????
+ ??????
??????
= ????????????
????????????
??????
− ??????
??????
= ?????? + ¿
?????? ∙ ????????????
??????
= ???????????? ⟹ ????????????
??????
= ????????????
???????????? − ??????
??????
= ?????? ⟹ ??????
??????
= ??????
{
????????????
??????
= ????????????
??????
??????
= ??????
{
?????? = ??????
?????? = ??????](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_3.png)
![Mustaqil bajarilgan topshiriqni tekshirish
Javob: 43. Tenglamalar sistemasini yeching. ?????? ¿
{
??????
?????? ?????? − ??????
= ????????????
??????
?????? ??????+ ???????????? + ?????? ??????
= ?????? {
??????
?????? ?????? − ??????
= ??????
??????
??????
?????? ??????+ ???????????? + ?????? ??????
= ??????
?????? {
?????? ?????? − ?????? = ??????
??????
??????
+ ???????????? + ??????
??????
= ??????
??????
??????
+ ?????? ∙ (?????? ?????? − ?????? )+ (?????? ?????? − ?????? )
??????
= ??????
?????? = ?????? ?????? − ??????
??????
??????
+ ?????? ??????
??????
− ?????? ?????? + ?????? ??????
??????
− ???????????? ?????? + ?????? = ??????
???????????? ??????
??????
− ???????????? ?????? + ?????? = ??????
?????? ?????? =
??????
????????????
; ?????? ?????? = ??????
?????? ??????=
− ????????????
????????????
?????? ?????? = ??????](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_4.png)
![Tenglamalarni taqribiy yechish
Agar ko‘phad kesma uchlarida turli ishorali
qiymatlarni qabul qilsa, ya’ni bo‘lsa, bu
kesma ichida tenglamaning kamida bitta
yechimi mavjud. Ya’ni shunday mavjudki](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_5.png)
![Tenglamalarni taqribiy yechish
Tenglamaning aynan bitta ildizini o‘z ichiga
olgan kesmani qaraylik.
Kesmani teng ikkiga bo‘lish usuli kesmani
hosil bo‘ladigan kesma uzunligi ξ aniqlikdan
kichik bo‘lgunicha teng ikkiga bo‘lishdan
iborat.
Buning uchun:
1) da ifodaning qiymati hisoblanadi.](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_6.png)
![Tenglamalarni taqribiy yechish
2) kesma teng ikkiga bo‘linadi, ya’ni
hisoblanadi;
3) ifodaning dagi qiymati hisoblanadi.
4) shart tekshiriladi;
5) agar bu shart bajarilsa, yangi kesmaning
chap chegarasi sifatida oldingi kesmaning
o‘rtasi olinadi, ya’ni deb olinadi (kesmaning
chap chegarasi o‘rtaga o‘tadi).](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_7.png)
![Tenglamalarni taqribiy yechish
6) agar bu shart bajarilmasa, yangi kesmaning
o‘ng chegarasi o‘rtaga o‘tadi, ya’ni deb olinadi
7) kesmani navbatdagi bo‘lishdan so‘ng shart
bajarilishi tekshiriladi.
8) agar bu shart bajarilsa, hisoblashlar
tugatiladi. Bunda taqribiy yechim sifatida ning
oxirgi hisoblangan qiymati olinadi. Agar bu
shart bajarilmasa, mazkur algoritmning 2-
qadamiga o‘tilib, hisoblashlar davom ettiriladi.](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_8.png)
![Haqiqiy ildiz yotgan oraliqni topish
tenglama ildizi yotgan oraliqni topish uchun
va hisoblanadi.
Berilgan tenglamaning ildizi uchun
tengsizlik o‘rinli bo‘ladi.
Berilgan tenglamaning kamida 1 ta ildizi
oraliqda joylashgan bo‘ladi.](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_9.png)
![Haqiqiy ildiz yotgan oraliqni topish
Bu ildizni taqriban topish uchun
va
Tengsizlikni qanoatlantiruvchi va butun sonlar
topiladi.](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_10.png)
![Mashqlar yechish
tenglama ildizi yotgan oraliqni toping.??????
??????
+
??????
??????
??????
??????
+
??????
??????
?????? +
??????
??????
= ??????
?????? =
??????
??????
; ?????? =
??????
??????
; ?????? =
??????
??????
⟹ ?????? = ??????????????????
{
??????
??????
;
??????
??????
;
??????
?????? }
= ?????? , ??????
Demak, oraliqda tenglamaning kamida 1 ta
ildizi bor.](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_11.png)
![Mashqlar yechish
Tenglama oraliqda ildizga ega emas, chunki
bo‘lsa,
bo‘ladi.
Demak, tenglama oraliqda tenglamaning
kamida 1 ta ildizi bor. Bu oraliqni kichraytirish
uchun butun sonlarni olamiz, ya’ni](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_12.png)
![Mashqlar yechish
Endi sonlarni
tenglamaga qo‘yib chiqamiz: ??????
??????
+
??????
??????
∙ ??????
??????
+
??????
??????
∙ ?????? +
??????
??????
= ?????? , ?????? > ??????
Javob:](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_13.png)
![Mashqlar yechish
44. 1) tenglama ildizi yotgan oraliqni toping.?????? = ?????? ; ?????? = ?????? ; ?????? = ?????? ⟹ ?????? = ?????????????????? {?????? ; ?????? ; ?????? }= ??????
Demak, oraliqda tenglamaning kamida 1 ta
ildizi bor.
Tenglama oraliqda ildizga ega emas, chunki
bo‘lsa,
bo‘ladi.](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_14.png)
![Mashqlar yechish
Demak, tenglama oraliqda tenglamaning
kamida 1 ta ildizi bor. Bu oraliqni kichraytirish
uchun butun sonlarni olamiz, ya’ni
Endi
sonlarni tenglamaga qo‘yib chiqamiz: (− ?????? )
??????
+ ?????? ∙(− ?????? )
??????
+ ?????? ∙(− ?????? )+ ?????? = ¿ − ???????????? + ???????????? − ???????????? + ?????? = − ???????????? < ??????](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_15.png)
![Mashqlar yechish(− ?????? )
??????
+ ?????? ∙(− ?????? )
??????
+ ?????? ∙(− ?????? )+ ?????? = ¿ − ???????????? + ???????????? − ???????????? + ?????? = − ???????????? < ??????
(− ?????? )
??????
+ ?????? ∙(− ?????? )
??????
+ ?????? ∙(− ?????? )+ ?????? = ¿ − ?????? + ???????????? − ???????????? + ?????? = − ?????? < ??????
(− ?????? )
??????
+ ?????? ∙(− ?????? )
??????
+ ?????? ∙(− ?????? )+ ?????? = ¿ − ?????? + ?????? − ?????? + ?????? = − ?????? < ??????
( ?????? )
??????
+ ?????? ∙ ( ?????? )
??????
+ ?????? ∙ ( ?????? ) + ?????? = ?????? > ??????
Javob:](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_16.png)
![Mashqlar yechish
45. 1) tenglama ildizi yotgan oraliqni toping.?????? = ?????? ; ?????? = ?????? , ?????? ; ?????? = ?????? , ?????? ⟹ ?????? = ?????????????????? {?????? ; ?????? , ?????? ; ?????? , ?????? }= ??????
Demak, oraliqda tenglamaning kamida 1 ta
ildizi bor.
Tenglama oraliqda ildizga ega emas, chunki
bo‘lsa,
bo‘ladi.
??????
??????
+ ?????? ??????
??????
+ ?????? , ?????? ?????? + ?????? , ?????? = ??????](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_17.png)
![Mashqlar yechish
Demak, tenglama oraliqda tenglamaning
kamida 1 ta ildizi bor. Bu oraliqni kichraytirish
uchun butun sonlarni olamiz, ya’ni
Endi
sonlarni tenglamaga qo‘yib chiqamiz: (− ?????? )
??????
+ ?????? ∙(− ?????? )
??????
+ ?????? ,?????? ∙(− ?????? )+ ?????? ,?????? = ¿ − ???????????? + ???????????? − ?????? ,?????? + ?????? ,?????? = − ???????????? < ??????](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_18.png)
![Mashqlar yechish(− ?????? )
??????
+ ?????? ∙(− ?????? )
??????
+ ?????? ,?????? ∙(− ?????? )+ ?????? ,?????? = ¿ − ?????? + ?????? − ?????? + ?????? ,?????? = − ?????? ,?????? < ??????
(− ?????? )
??????
+ ?????? ∙(− ?????? )
??????
+ ?????? ,?????? ∙(− ?????? )+ ?????? ,?????? = ¿ − ?????? + ?????? − ?????? ,?????? + ?????? ,?????? = ??????
??????
??????
+ ?????? ∙ ??????
??????
+ ?????? , ?????? ∙ ?????? + ?????? , ?????? = ?????? , ?????? > ??????
Javob:](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_19.png)
![Mustaqil yechish uchun topshiriq
Darslikning 76- betidagi 44, 45, 46- mashqlar-
ning juft tartibdagi misollarini yechish](/data/documents/0118fc7b-21b3-43ed-a3ec-41ea24e5a90d/page_20.png)
Mavzu: Tenglamalarni taqribiy yechish
Mustaqil bajarilgan topshiriqni tekshirish Javob:42. Tenglamalar sistemasini yeching. ?????? ¿ { ?????? ?????? + ?????? ?????? = ?????????????????? ?????? ?????? ??????+ ?????? ???????????? − ?????? ?????? = ?????? { ?????? ?????? + ?????? ?????? = ?????? ?????? ?????? ?????? ??????+ ?????? ???????????? − ?????? ?????? = ?????? ?????? { ?????? + ?????? ?????? = ?????? ?????? ?????? + ?????? ???????????? − ?????? ?????? = ?????? (?????? − ?????? ?????? ) ?????? + ?????? ?????? ∙ (?????? − ?????? ?????? )− ?????? ?????? = ?????? ⟹ ?????? = ?????? − ?????? ?????? ?????? − ???????????? ?????? + ?????? ?????? ?????? + ?????? ?????? − ?????? ?????? ?????? − ?????? ?????? = ?????? ?????? ?????? + ?????? − ?????? = ?????? ?????? ?????? = − ?????? ; ?????? ?????? = ?????? ?????? ?????? = ?????? ?????? ?????? = ??????
Mustaqil bajarilgan topshiriqni tekshirish Javob:42. Tenglamalar sistemasini yeching. ?????? ¿ { ???????????? ?????? + ?????? ?????? = ???????????? ???????????? ?????? − ?????? ?????? = ?????? + ¿ ?????? ∙ ???????????? ?????? = ???????????? ⟹ ???????????? ?????? = ???????????? ???????????? − ?????? ?????? = ?????? ⟹ ?????? ?????? = ?????? { ???????????? ?????? = ???????????? ?????? ?????? = ?????? { ?????? = ?????? ?????? = ??????
Mustaqil bajarilgan topshiriqni tekshirish Javob: 43. Tenglamalar sistemasini yeching. ?????? ¿ { ?????? ?????? ?????? − ?????? = ???????????? ?????? ?????? ??????+ ???????????? + ?????? ?????? = ?????? { ?????? ?????? ?????? − ?????? = ?????? ?????? ?????? ?????? ??????+ ???????????? + ?????? ?????? = ?????? ?????? { ?????? ?????? − ?????? = ?????? ?????? ?????? + ???????????? + ?????? ?????? = ?????? ?????? ?????? + ?????? ∙ (?????? ?????? − ?????? )+ (?????? ?????? − ?????? ) ?????? = ?????? ?????? = ?????? ?????? − ?????? ?????? ?????? + ?????? ?????? ?????? − ?????? ?????? + ?????? ?????? ?????? − ???????????? ?????? + ?????? = ?????? ???????????? ?????? ?????? − ???????????? ?????? + ?????? = ?????? ?????? ?????? = ?????? ???????????? ; ?????? ?????? = ?????? ?????? ??????= − ???????????? ???????????? ?????? ?????? = ??????
Tenglamalarni taqribiy yechish Agar ko‘phad kesma uchlarida turli ishorali qiymatlarni qabul qilsa, ya’ni bo‘lsa, bu kesma ichida tenglamaning kamida bitta yechimi mavjud. Ya’ni shunday mavjudki