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zmudz

  • one year ago

Prove that if \(x,y,z\) are positive real numbers then the following inequality holds \( \frac {x+y}{x^2+y^2} + \frac {y+z}{y^2+z^2} + \frac {z+x}{z^2+x^2} \leq \frac 1x + \frac 1y + \frac 1z . \)

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  1. jtvatsim
    • one year ago
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    Have you attempted anything already? Just so I don't go down a dead end path if you've already tried it. :)

  2. zmudz
    • one year ago
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    no, I am stuck :/

  3. jtvatsim
    • one year ago
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    k, what class is this for so I know what level of math to use?

  4. zmudz
    • one year ago
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    precalculus

  5. jtvatsim
    • one year ago
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    alright.

  6. zmudz
    • one year ago
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    thank you!

  7. jtvatsim
    • one year ago
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    Right now, I am going to try to get the fractions to have the same denominators, the algebra is very messy for now... but I'm going to see where it takes me. I'll do this on scrap paper, rather than on the computer. But know that I am trying to solve it. ;)

  8. zmudz
    • one year ago
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    sounds good, I appreciate this a lot!

  9. jtvatsim
    • one year ago
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    hmm... this one is nasty... I'm trying a new approach... :)

  10. jtvatsim
    • one year ago
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    Almost have something...

  11. jtvatsim
    • one year ago
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    Ahh... so close. How have your classes been proving things in precalculus?

  12. jtvatsim
    • one year ago
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    Because I could make an argument using around 6-8 cases, but it's a bit tedious... :)

  13. jtvatsim
    • one year ago
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    Sorry, I'm struggling a bit. I might just type up a pdf to show the solution. It's a bit messy to look at, but I can't see a simpler method yet.

  14. zmudz
    • one year ago
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    AM/GM inequality, maxima minima, induction, mean inequality chain

  15. zmudz
    • one year ago
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    also cauchy schwartz

  16. zmudz
    • one year ago
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    take your time, thanks. pdf and any help at all is great :)

  17. anonymous
    • one year ago
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    sorry to get off topic, how do you type out math latex in a pdf?

  18. jtvatsim
    • one year ago
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    I use overleaf.com it's web-based and allows you to download a pdf after typing LaTeX.

  19. anonymous
    • one year ago
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    thankyou

  20. jtvatsim
    • one year ago
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    Here's my attempt, I didn't finish the proof, because my method was brute force and very tiring...

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  21. IrishBoy123
    • one year ago
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    .

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