Can You Solve This Radical Expression? | Math Olympiad Questions

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  • Опубліковано 20 січ 2025

КОМЕНТАРІ • 4

  • @abbeydudeuk
    @abbeydudeuk 7 днів тому

    Iska use kya hai?

  • @walterwen2975
    @walterwen2975 5 днів тому

    Math Olympiad Questions: {(³√100 - 1)/[3(³√10) + 3]}⁵ =?
    Let: a = ³√10; (³√100 - 1)/[3(³√10) + 3] = (a² - 1)/(3a + 3) = (a - 1)/3
    {(³√100 - 1)/[3(³√10) + 3]}⁵ = [(a - 1)/3]⁵ = [(a - 1)⁵]/(3⁵)
    (a - 1)⁵ = a⁵ - 5a⁴ + 10a³ - 10a² + 5a - 1
    = ³√10⁵ - 5(³√10)⁴ + 10(³√10)³ - 10(³√10)² + 5(³√10) - 1
    = 10(³√10²) - 50(³√10) + 100 - 10(³√10²) + 5(³√10) - 1 = 99 - 45(³√10)
    {(³√100 - 1)/[3(³√10) + 3]}⁵ = [99 - 45(³√10)]/3⁵ = [11 - 5(³√10)]/27
    Answer check:
    {(³√100 - 1)/[3(³√10) + 3]}⁵ = [(a - 1)/3]⁵ = [(√10 - 1)/3]⁵ = (1.154/3)⁵ = 0.385⁵ = 0.0084
    [11 - 5(³√10)]/27 = [11 - 5(2.154)]/27 = 0.228/27 = 0.084; Confirmed
    The calculation was achieved on a smartphone with a standard calculator app
    Final answer:
    {(³√100 - 1)/[3(³√10) + 3]}⁵ = [(³√10 - 1)/3]⁵ = [11 - 5(³√10)]/27