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Math Help - inequalities II

  1. #1
    Junior Member
    Joined
    May 2009
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    29

    inequalities II

    Prove that if real numbers a, b and c satisfy

    a + b + c > 0,

    ab + ac + bc > 0

    and

    abc > 0,

    then each of a, b and c is positive.
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  2. #2
    Junior Member
    Joined
    Jun 2010
    Posts
    44
    I'll give you a tip: a b c are the roots of the 3rd degree polynomial a X^3 + b X^2 + c X + d

    S1 = a + b + c = -b/a > 0
    S2 = ab + ac + bc = c/a > 0
    S3 = abc = -d/a > 0

    i'll to think a bit for the rest of the problem
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