Asosiy kontent
Algebra II
Course: Algebra II > Unit 2
Lesson 1: Mavhum sonlar nima?- Mavhum sonlar mavzusiga kirish
- Mavhum sonlar mavzusiga kirish
- Manfiy sonlarning ildizlarini soddalashtirish
- Manfiy sonlarning ildizlarini soddalashtiring.
- Mavhum birlikning darajalari
- Mavhum birlikning darajalari
- Mavhum birlikning darajalari
- i birlik -1 ning ildizi sifatida
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Mavhum birlikning darajalari
Mavhum birlik i ning darajasini qanday soddalashtirishni oʻrganing. Masalan, i²⁷ ni -i kabi soddalashtiring.
Bilamizki, i, equals, square root of, minus, 1, end square root va i, squared, equals, minus, 1.
Biroq i, cubed va i, start superscript, 4, end superscript haqida-chi? i ning boshqa butun darajalari-chi? Bularni qanday hisoblaymiz?
i, cubed va i, start superscript, 4, end superscriptni topish
Darajalar xossasi bu yerda yordam berishi mumkin! i ning darajasini hisoblayotganda biz toʻgʻri deb bilgan darajalarning xossalarini haqiqiy sonlar tizimida qoʻllashimiz mumkin, agar darajalar butun son boʻlsa.
Shunga asoslanib, i, cubed va i, start superscript, 4, end superscript ni topamiz.
Bizga maʼlumki, i, cubed, equals, i, squared, dot, i. Ammo i, squared, equals, minus, 1 boʻlar ekan, biz shuni kuzatishimiz mumkin:
Shuningdek, i, start superscript, 4, end superscript, equals, i, squared, dot, i, squared. Yana i, squared, equals, minus, 1 dan foydalanib, quyidagi natijaga erishamiz:
i ning darajalari
Shu yoʻsinda davom etamiz! Bizga tanish usuldan foydalanib i ning navbatdagi 4 ta darajasini topamiz:
Natijalarni jadvalda yozamiz:
i, start superscript, 1, end superscript | i, squared | i, cubed | i, start superscript, 4, end superscript | i, start superscript, 5, end superscript | i, start superscript, 6, end superscript | i, start superscript, 7, end superscript | i, start superscript, 8, end superscript |
---|---|---|---|---|---|---|---|
start color #11accd, i, end color #11accd | start color #1fab54, minus, 1, end color #1fab54 | start color #7854ab, minus, i, end color #7854ab | start color #e07d10, 1, end color #e07d10 | start color #11accd, i, end color #11accd | start color #1fab54, minus, 1, end color #1fab54 | start color #7854ab, minus, i, end color #7854ab | start color #e07d10, 1, end color #e07d10 |
Darajalarning ketma-ketligi
Jadvaldan, i ning darajalari start color #11accd, i, end color #11accd, start color #1fab54, minus, 1, end color #1fab54, start color #7854ab, minus, i, end color #7854ab va start color #e07d10, 1, end color #e07d10 ketma-ketlikda ketishi koʻrinadi.
Bu ketma-ketlikdan foydalanib i, start superscript, 20, end superscript topa olamizmi? Keling, urinib koʻramiz.
Quyidagi qatorda dastlabki 20 ta son keltirilgan:
start color #11accd, i, end color #11accd, start color #1fab54, minus, 1, end color #1fab54, start color #7854ab, minus, i, end color #7854ab, start color #e07d10, 1, end color #e07d10, start color #11accd, i, end color #11accd, start color #1fab54, minus, 1, end color #1fab54, start color #7854ab, minus, i, end color #7854ab, start color #e07d10, 1, end color #e07d10, start color #11accd, i, end color #11accd, start color #1fab54, minus, 1, end color #1fab54, start color #7854ab, minus, i, end color #7854ab, start color #e07d10, 1, end color #e07d10, start color #11accd, i, end color #11accd, start color #1fab54, minus, 1, end color #1fab54, start color #7854ab, minus, i, end color #7854ab, start color #e07d10, 1, end color #e07d10, start color #11accd, i, end color #11accd, start color #1fab54, minus, 1, end color #1fab54, start color #7854ab, minus, i, end color #7854ab, start color #e07d10, 1, end color #e07d10
Bu mantiqqa koʻra, i, start superscript, 20, end superscript start color #e07d10, 1, end color #e07d10ga teng boʻlishi kerak. Keling, darajalar yordamida buni koʻrib chiqamiz. Yodingizda boʻlsin, biz bu yerda darajalarning xossalaridan, xuddi haqiqiy sonlar bilan boʻlgani kabi foydalanishimiz mumkin!
Har qanday holatda ham i, start superscript, 20, end superscript, equals, 1 ekanini koʻramiz.
i ning darajalari
Biz endi i, start superscript, 138, end superscriptni topishga urinib koʻraylik. Biz ketma-ketlik roʻyxatini 138, start superscript, start text, c, h, i, end text, end superscript hadda tuzishimiz mumkin start color #11accd, i, end color #11accd, start color #1fab54, minus, 1, end color #1fab54, start color #7854ab, minus, i, end color #7854ab, start color #e07d10, 1, end color #e07d10,... , ammo bu juda koʻp vaqt oladi!
Ahamiyat bering, i, start superscript, 4, end superscript, equals, 1, i, start superscript, 8, end superscript, equals, 1, i, start superscript, 12, end superscript, equals, 1 va hokazo. Boshqacha aytganda, i ning darajasi 4 ning karralisi boʻlganda 1ga teng boʻladi.
Biz ushbu maʼlumotdan i, start superscript, 138, end superscript ni soddalashtirishga yordam berish maqsadida uni darajalarning xossalari bilan birga qoʻllashimiz mumkin.
Misol
i, start superscript, 138, end superscript ni soddalashtiring.
Yechim
138 soni 4 ning karralisi emas, 136 esa karrali! Bundan foydalanib i, start superscript, 138, end superscriptni soddalashtiramiz.
Shu bois i, start superscript, 138, end superscript, equals, minus, 1.
Endi nega i, start superscript, 138, end superscript ifodani i, start superscript, 136, end superscript, dot, i, squared koʻrinishga keltirganimizni soʻrashingiz mumkin.
Agar asl daraja 4ga karrali boʻlmasa, u holda undan kichikroq boʻlgan eng yaqin karralisini topish darajani, shunchaki i, start superscript, 4, end superscript, equals, 1 haqidagi maʼlumotdan foydalanib, i, i, squared, yoki i, cubed gacha soddalashtirish imkonini beradi.
Agar siz asl darajani 4 ga boʻlsangiz bu sonni topish oson kechadi. Bu shunchaki 4 marta boʻlinma (qoldiqsiz).
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