Mathematical proof

  • #1
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Homework Statement


Let a,b be in the positive reals. Prove a/b+b/a is >=2

Homework Equations




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?
 

Answers and Replies

  • #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?
 
  • #3
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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?
I feel like this is related to the law of cosines
 
  • #4
jbriggs444
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I feel like this is related to the law of cosines
Your powers of pattern recognition are good, but there is another formula involving a2, b2 and 2ab that is simpler yet.
 
  • #5
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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.
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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