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Basic math proof by contradiction

  1. Mar 9, 2008 #1
    [SOLVED] basic math proof by contradiction

    1. The problem statement, all variables and given/known data

    prove: If a and b are positive numbers, a/b +b/a>=2

    2. Relevant equations



    3. The attempt at a solution

    by contradiction (a^2+b^2)/ab<2 and got lost
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 9, 2008 #2

    Dick

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    Homework Helper

    If (a^2+b^2)/ab<2 then a^2+b^2<2ab. So a^2+b^2-2ab<0. But a^2+b^2-2ab=(a-b)^2<0. What could be wrong with that?
     
  4. Mar 9, 2008 #3
    thanks it was that easy
     
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