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math

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if the arithmetic mean of 2 positive numbers (a and b) is 16 and their geometric mean is 12, find the exact value of a^3+b^3.

  • math -

    AM = (a+b)/2
    GM = √ab

    a+b = 32
    ab = 144

    (a+b)^2 = (a^2 + b^2 + 2ab)
    1024 = a^2 + b^2 + 288
    a^2 + b^2 = 736

    a^3 + b^3 = (a+b)(a^2 - ab + b^2)
    = 32(736 - 144) = 18944

    Not bad, for not knowing either a or b.

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