zmudz
  • zmudz
Prove that if \(x,y,z\) are positive real numbers then the following inequality holds \( \frac {x+y}{x^2+y^2} + \frac {y+z}{y^2+z^2} + \frac {z+x}{z^2+x^2} \leq \frac 1x + \frac 1y + \frac 1z . \)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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jtvatsim
  • jtvatsim
Have you attempted anything already? Just so I don't go down a dead end path if you've already tried it. :)
zmudz
  • zmudz
no, I am stuck :/
jtvatsim
  • jtvatsim
k, what class is this for so I know what level of math to use?

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More answers

zmudz
  • zmudz
precalculus
jtvatsim
  • jtvatsim
alright.
zmudz
  • zmudz
thank you!
jtvatsim
  • jtvatsim
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. ;)
zmudz
  • zmudz
sounds good, I appreciate this a lot!
jtvatsim
  • jtvatsim
hmm... this one is nasty... I'm trying a new approach... :)
jtvatsim
  • jtvatsim
Almost have something...
jtvatsim
  • jtvatsim
Ahh... so close. How have your classes been proving things in precalculus?
jtvatsim
  • jtvatsim
Because I could make an argument using around 6-8 cases, but it's a bit tedious... :)
jtvatsim
  • jtvatsim
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.
zmudz
  • zmudz
AM/GM inequality, maxima minima, induction, mean inequality chain
zmudz
  • zmudz
also cauchy schwartz
zmudz
  • zmudz
take your time, thanks. pdf and any help at all is great :)
anonymous
  • anonymous
sorry to get off topic, how do you type out math latex in a pdf?
jtvatsim
  • jtvatsim
I use overleaf.com it's web-based and allows you to download a pdf after typing LaTeX.
anonymous
  • anonymous
thankyou
jtvatsim
  • jtvatsim
Here's my attempt, I didn't finish the proof, because my method was brute force and very tiring...
1 Attachment
IrishBoy123
  • IrishBoy123
.

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