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Math Help - a question......

  1. #1
    Junior Member
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    a question......

    a.b-c=4

    b.c-a=3

    in equality, a, b, c are positive integers.

    What is total of a+b+c minumum?
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  2. #2
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    a.b-c=4

    b.c-a=3

    add the two equations together:

    ab+bc-a-c=7

    move things around:

    ab-a+bc-c=7

    factor:

    a(b-1)+c(b-1)=7

    factor again:

    (a+c)(b-1)=7

    hmm, 7 is a prime number though and so cannot have two integer factors, unless b-1 = 1 and a+c=7 or b-1=7 and a+c=1 (which means that in this case either a or c must be zero, I don't know if you consider that a positive integer)

    In the first case: b = 2 and a+c=7

    So if we add those two together: a+b+c=9


    In the second case: b = 8 and a+c=1

    So if we add those two together: a+b+c=9

    So the answer is: \boxed{a+b+c=9}
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