- #1

- 189

- 4

## 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?

- 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

Science Advisor

Homework Helper

- 9,603

- 4,257

- #3

- 189

- 4

I feel like this is related to the law of cosines

- #4

jbriggs444

Science Advisor

Homework Helper

- 9,603

- 4,257

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

- 4

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

- Last Post

- Replies
- 2

- Views
- 239

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 31

- Views
- 1K

- Last Post

- Replies
- 3

- Views
- 808

- Last Post

- Replies
- 4

- Views
- 981

- Last Post

- Replies
- 17

- Views
- 590

- Replies
- 9

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 594

- Last Post

- Replies
- 8

- Views
- 747

- Replies
- 3

- Views
- 7K