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Math Help - The difference between two positive integers is 4 and ......

  1. #1
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    The difference between two positive integers is 4 and ......

    Hi guys, I have a question from my workbook which i don't understand and know how to do.

    Question: The difference between two positive integers is 4 and the difference between this reciprocals is (1)/(48). Find the integers.

    Ok so I have form this two equations,

    Let x be first integer
    Let y be second integer

    x - y = 4
    (1)/(x) - (1)/(y) = (1)/(48)

    But I don't know how to continue from there, I don't even know whether my equation is the right one.

    Please do help
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  2. #2
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    Your equations are correct.

    From equation 1, it is clear that x = y + 4.

    So substitute this into equation 2 to get

    1/(y + 4) - 1/y = 1/48

    y/[y(y + 4)] - (y + 4)/[y(y + 4)] = 1/48

    [y - (y + 4)]/[y(y + 4)] = 1/48

    -4/[y(y + 4)] = 1/48

    -4 = [y(y + 4)]/48

    -192 = y(y + 4)

    Now expand and set the equation equal to 0 and solve the resulting quadratic.
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  3. #3
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    I managed to get to here but, how do i solve "-192 = y^2 + 4y"
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  4. #4
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    Quote Originally Posted by FailInMaths View Post
    I managed to get to here but, how do i solve "-192 = y^2 + 4y"
    y^2 + 4y + 192 = 0 is a quadratic equation. When all else fails, use the quadratic formula.

    -Dan

    Edit: Interesting. I was about to say that this factors, but I'm getting only complex zeros.

    Edit II: Ah. I have it now. There was an understandable mistake. Notice that if x is the larger number then 1/x - 1/y is negative. So your two equations are
    x - y = 4
    1/x - 1/y = -1/48

    This gives a reasonable solution set.
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  5. #5
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    Quote Originally Posted by FailInMaths View Post
    Question: The difference between two positive integers is 4 and the difference between this reciprocals is (1)/(48). Find the integers.
    Ok so I have form this two equations,
    Let x be first integer Let y be second integer
    x - y = 4
    (1)/(x) - (1)/(y) = (1)/(48)
    Quote Originally Posted by Prove It View Post
    Your equations are correct.
    -192 = y(y + 4)
    The solutions to the above are two complex numbers.
    The reason being is that your equations are not correct.
    If you have x-y=4 where x~\&~y are positive integers then that implies that x>y.
    Thus you need to have \frac{1}{y}-\frac{1}{x} =\frac{1}{48} because we need  \frac{1}{y}>\frac{1}{x}.

    Now use the same ideas in post #2.
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