- #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?
I feel like this is related to the law of cosinesThose a's and b's in the denominator are pesky. Why not multiply through by ab and see what that gives you?
Your powers of pattern recognition are good, but there is another formula involving a2, b2 and 2ab that is simpler yet.I feel like this is related to the law of cosines
oh hahahahahah (a-b)^2>=0Your powers of pattern recognition are good, but there is another formula involving a2, b2 and 2ab that is simpler yet.