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Math Help - find the mean

  1. #1
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    find the mean

    If the geometric mean of a and b is 10 and the harmonic mean of a and b is 8, find the value of the following without determining the values of a and b.

    1/a + 1/b
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  2. #2
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    Hello, Mr_Green!

    Are you sure of the wording of the problem?
    . . It seems to be much too simple.


    If the geometric mean of a and b is 10 . ← not needed
    and the harmonic mean of a and b is 8,
    find the value of (1/a + 1/b) without determining the values of a and b.

    . . . . . . . . . . . . . 2
    We are given: . -------- . = . 8
    . . . . . . . . . . . .1 . . 1
    . . . . . . . . . . . .-- + --
    . . . . . . . . . . . .a . . b


    . . . . . .1 . . 1 . . . . 1
    Then: . -- + -- . = . --
    . . . . . .a . . b . . . . 4

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  3. #3
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    i meant:


    1/(a^2) + 1/(b^2)
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  4. #4
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    Hello again, Mr_Green!

    If the geometric mean of a and b is 10 and the harmonic mean of a and b is 8,
    find the value of: .1/aČ + 1/bČ
    We are given: .√(ab) = 10 . . ab = 100 . . 2/ab = 1/50 .[1]


    I have already shown that: .1/a + 1/b .= .1/4

    Square both sides: .1/aČ + 2/ab + 1/bČ .= .1/16
    . . . . . . . . . . . . . . . . . . . .
    Substitute [1]: . . . 1/aČ + 1/50 +1/bČ .= .1/16


    Therefore: .1/aČ + 1/bČ .= .1/16 - 1/50 .= .17/400

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