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Mathematical proof

  1. Apr 20, 2016 #1
    1. The problem statement, all variables and given/known data
    Let a,b be in the positive reals. Prove a/b+b/a is >=2
    2. Relevant equations


    3. The attempt at a solution
    I have no idea. Maybe add the two ratios: (a^2+b^2)/a*b and then try to analyze separately the numerator and denominator?
     
  2. jcsd
  3. Apr 20, 2016 #2

    jbriggs444

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    Those a's and b's in the denominator are pesky. Why not multiply through by ab and see what that gives you?
     
  4. Apr 20, 2016 #3
    I feel like this is related to the law of cosines
     
  5. Apr 20, 2016 #4

    jbriggs444

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    Your powers of pattern recognition are good, but there is another formula involving a2, b2 and 2ab that is simpler yet.
     
  6. Apr 20, 2016 #5
    oh hahahahahah (a-b)^2>=0
    when a=b (a-b)^2=0
    when a!=b (a-b)^2>0
    so (a-b)^2>=0
     
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