Alisher Math Academy
Talabalar olimpiadasi 31.03.2024.pdf
Bugun 00:00 da yechimlar qabul qilish to'xtatiladi. Biz yechimlaringizni kutyapmiz🙂
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Category A.xlsx - Category A code.pdf
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📊 OMOUS-2024 olimpiadasining umumiy natijalari!
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Darajasi n ga teng bo'lgan haqiqiy koeffitsiyentli P(x)>0 (x€R) ko'phad berilgan. Isbotlang: P(x)+P'(x)+P''(x)+...+Pⁿ(x)>0 ixtiyoriy x€R uchun.
@MathOliy1
@MathOliy1
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#Savol #Algebra
R halqada x∈R uchun x⁶=x tenglik o'rinli bo'lsa, R kommutativ halqa ekanligini isbotlang.
Let R be a ring such that x⁶=x for all x∈R. Prove that R is commutative.
@MathOliy1
R halqada x∈R uchun x⁶=x tenglik o'rinli bo'lsa, R kommutativ halqa ekanligini isbotlang.
Let R be a ring such that x⁶=x for all x∈R. Prove that R is commutative.
@MathOliy1
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#Savol #Chiziqli_algebra
A,B∈M n×n (R) matritsalar uchun A²=A, B²=B va det(A+3B)=0 tengliklar o'rinli bo'lsa, det(3A+B) ni toping.
Let A,B∈M n×n (R) be two matrices such that A²=A, B²=B and det(A+3B)=0. Find det(3A+B).
@MathOliy1
A,B∈M n×n (R) matritsalar uchun A²=A, B²=B va det(A+3B)=0 tengliklar o'rinli bo'lsa, det(3A+B) ni toping.
Let A,B∈M n×n (R) be two matrices such that A²=A, B²=B and det(A+3B)=0. Find det(3A+B).
@MathOliy1
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#Savol #Sonlar_nazariyasi
Har bir n natural son uchun 2021ⁿ soni ikki natural sonlarning kvadratlari farqi(ayirmasi) sifatida ifodalanishini ko'rsating.
Show that 2021ⁿ can be expressed as difference of two squares of natural numbers for every positive integer n (i.e. n=1,2,...).
@MathOliy1
Har bir n natural son uchun 2021ⁿ soni ikki natural sonlarning kvadratlari farqi(ayirmasi) sifatida ifodalanishini ko'rsating.
Show that 2021ⁿ can be expressed as difference of two squares of natural numbers for every positive integer n (i.e. n=1,2,...).
@MathOliy1
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