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Math Help - If a, b and c are positive real numbers, prove that 4(a + b) ≥ (a + b)

  1. #1
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    If a, b and c are positive real numbers, prove that 4(a + b) ≥ (a + b)

    If a, b and c are positive real numbers, prove that 4(a + b) ≥ (a + b) & that 9(a + b + c) ≥ (a + b + c)
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  2. #2
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    Quote Originally Posted by Mozart View Post
    If a, b and c are positive real numbers, prove that 4(a + b) ≥ (a + b) & that 9(a + b + c) ≥ (a + b + c)
    for the first one;
     4a^3+4b^3\geq a^3+3a^2b+3ab^2+b^3
    \Longleftrightarrow 3a^3+3b^3\geq 3a^2b+3ab^2
    \Longleftrightarrow a^3+b^3\geq a^2b+ab^2
    \Longleftrightarrow (a+b)(a^2-ab+b^2)\geq (a+b)(ab)
    \Longleftrightarrow a^2-ab+b^2\geq ab
    \Longleftrightarrow a^2-2ab+b^2\geq 0
    \Longleftrightarrow (a-b)^2\geq 0
    Last edited by bram kierkels; October 2nd 2009 at 02:46 AM.
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  3. #3
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    that's wrong proof.

    to fix it, in each step you need to add an \iff.
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