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Let α and β be two numbers where α < β. The geometric mean of these numbers exceeds the smaller number α by 12 and the arithmetic mean of the same numbers is smaller by 24 than the larger number β, then the value of |β−α| is
    Correct answer is '48'. Can you explain this answer?
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    Let α and β be two numbers where α < β. The g...


    Given Data:
    - Let α and β be two numbers where α < β.
    - Geometric mean of the numbers = √(αβ) = α + 12
    - Arithmetic mean of the numbers = (α + β)/2 = β - 24

    Calculating the Values:
    Let's solve the given equations:
    1. √(αβ) = α + 12
    Squaring both sides,
    αβ = (α + 12)^2
    αβ = α^2 + 24α + 144

    2. (α + β)/2 = β - 24
    Simplifying,
    α + β = 2β - 48
    α = β - 48

    Substitute the value of α in terms of β in the first equation:
    (β - 48)β = (β - 48)^2 + 24(β - 48) + 144
    β^2 - 48β = β^2 - 96β + 2304 + 24β - 1152 + 144
    0 = -120β + 1296

    Solving for |β - α|:
    From the above equation, β = 10.8
    Substitute β back into α = β - 48, we get α = -37.2

    Therefore, |β - α| = |10.8 - (-37.2)| = 48

    Hence, the value of |β - α| is 48.
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    Community Answer
    Let α and β be two numbers where α < β. The g...
    Given, α & β be two number where α < />
    ∵The geometric mean of these numbers exceeds the smaller number α by 12.
    And the arithmetic mean of the same numbers is smaller by 24 than the number β.
    By solving Equations. (i) & (ii)(i) & (ii), we get
    α = 6, β = 54
    ∴|β − α| = |54 − 6| = 48
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    Let α and β be two numbers where α < β. The geometric mean of these numbers exceeds the smaller number α by 12 and the arithmetic mean of the same numbers is smaller by 24 than the larger number β, then the value of |β−α| isCorrect answer is '48'. Can you explain this answer?
    Question Description
    Let α and β be two numbers where α < β. The geometric mean of these numbers exceeds the smaller number α by 12 and the arithmetic mean of the same numbers is smaller by 24 than the larger number β, then the value of |β−α| isCorrect answer is '48'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let α and β be two numbers where α < β. The geometric mean of these numbers exceeds the smaller number α by 12 and the arithmetic mean of the same numbers is smaller by 24 than the larger number β, then the value of |β−α| isCorrect answer is '48'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let α and β be two numbers where α < β. The geometric mean of these numbers exceeds the smaller number α by 12 and the arithmetic mean of the same numbers is smaller by 24 than the larger number β, then the value of |β−α| isCorrect answer is '48'. Can you explain this answer?.
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