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Math Help - geometric mean

  1. #1
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    geometric mean

    The arithmetic mean of 1/(a+b) and 1/(b+c) is 1/(a+c)

    Find in terms of b , the arithmetic mean of a^2 and c^2 .
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  2. #2
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    Arithmetic mean implies

    \frac{\frac{1}{a+b} + \frac{1}{b+c}}{2} = \frac{1}{a+c}

    In this equation find a common denominator for the LHS, cross multiply then simplify.

    After some cancelling you will be left with a^2+c^2 = \dots

    Then divide both sides by 2 and your answer will appear.

    Spoiler:
    b^2
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