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

Please help me this as soon as possible.Thanks!

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

Please help me this as soon as possible.Thanks!

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TopNewestLooks like an application of Cauchy's/Titu's – Sharky Kesa · 6 days, 10 hours ago

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– Anik Mandal · 6 days, 10 hours ago

Did you get the result?Log in to reply

@Sharky Kesa – Anik Mandal · 1 week ago

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

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Are you sure the problem is correct, because x=0.5 and y=\(-0.5\) are not satisfying the condition. – Harsh Shrivastava · 1 week ago

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– Anik Mandal · 1 week ago

They are not satisfying first condition only.Log in to reply

– Harsh Shrivastava · 1 week ago

Oh sorry I misread x^2 +y^2 as x+y.Log in to reply

– Anik Mandal · 1 week ago

I believe this was an RMO problem of some year.Anyways you'll have your RMO this Sunday right?Log in to reply

– Harsh Shrivastava · 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.Log in to reply

– Anik Mandal · 1 week ago

Ok!Are you there on Slack or hangouts?I mean are you active?Log in to reply

– Harsh Shrivastava · 1 week ago

Yeah, wbu?Log in to reply

– Anik Mandal · 1 week ago

Same.Log in to reply

@Harsh Shrivastava Can you help? – Anik Mandal · 1 week ago

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