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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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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