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x and y are positive real numbers that satisfy logxy+logyx=174 and xy=2883√. If x+y=a+bc√, where a, b and c are positive integers and c is not divisible by the square of any prime, what is the value of a+b+c?

  • maths -

    Having posted the same problem three times and not
    getting a response should have given you a hint, that there might be something wrong with the question, or the way you typed it.
    e.g. 2883√ makes no sense, the √ is not written behind the number
    which makes x+y = a + bc√ completely ambiguous.

    I will start it off:

    logxy+logyx=174
    the way you typed it .....

    2 log xy = 174
    log xy = 72
    xy = 10^72 ---- huge!!
    but assuming xy = √2883
    so √2883 = 10^72 ??? , not likely

    I have a feeling you meant:

    logxy + logyx = 174

  • maths -

    logxy + logyx = 17/4

  • maths -

    log y base x + log x base y =17/4

    sorry for the typo.

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