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# A doubt!

Let $$x$$ and $$y$$ be real numbers such that $$x^2+y^2=1$$ .Prove that $\dfrac{1}{1+x^2}+ \dfrac{1}{1+y^2} + \dfrac{1}{1+xy} \geq \frac{3}{1+(\dfrac{x+y}{2})^2}$

Note by Anik Mandal
1 week ago

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Looks like an application of Cauchy's/Titu's · 6 days, 10 hours ago

Did you get the result? · 6 days, 10 hours ago

@Sharky Kesa · 1 week ago

Setting xy=t maybe fruitful, but I have not tried it. · 1 week ago

Are you sure the problem is correct, because x=0.5 and y=$$-0.5$$ are not satisfying the condition. · 1 week ago

They are not satisfying first condition only. · 1 week ago

Oh sorry I misread x^2 +y^2 as x+y. · 1 week ago

I believe this was an RMO problem of some year.Anyways you'll have your RMO this Sunday right? · 1 week ago

Bro I'll try this problem tonight because I have to goto Fiitjee after some time, and need to study chemistry, The problem seems to be tricky. · 1 week ago

Ok!Are you there on Slack or hangouts?I mean are you active? · 1 week ago

Yeah, wbu? · 1 week ago

Same. · 1 week ago