- #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?

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- Thread starter TheMathNoob
- Start date

- #1

- 189

- 4

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

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

jbriggs444

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- #3

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I feel like this is related to the law of cosines

- #4

jbriggs444

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Your powers of pattern recognition are good, but there is another formula involving aI feel like this is related to the law of cosines

- #5

- 189

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oh hahahahahah (a-b)^2>=0Your powers of pattern recognition are good, but there is another formula involving a^{2}, b^{2}and 2ab that is simpler yet.

when a=b (a-b)^2=0

when a!=b (a-b)^2>0

so (a-b)^2>=0

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