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I try to prove this :

Let $x,y,z>0$ such that $xyz=1$ then we have : $$\frac{x}{x^{10}+1}+\frac{y}{y^{10}+1}+\frac{z}{z^{10}+1}\leq \frac{3}{2}$$

You can follow my proof here.It works too but I have some doubt for the end so my real question is :

How to prove that the maximum of the function below is $1.5$ : $$f(x)=\frac{2x^9}{x^{10}+1}+\frac{x^2}{x^{20}+1}$$

Thanks for your interest .

max8128
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    Do you use the second yellow box statement in your proof of the main inequaity of the post? If so how to know your proof "works"? – coffeemath Aug 17 '19 at 12:59
  • So your real question is whether your own answer in the other thread is correct, and if not, how to fix it? – Martin R Aug 17 '19 at 19:53

0 Answers0