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

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

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
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

Have you attempted anything already? Just so I don't go down a dead end path if you've already tried it. :)
no, I am stuck :/
k, what class is this for so I know what level of math to use?

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

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

Not the answer you are looking for?

Search for more explanations.

Ask your own question