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Inequality Problem

Given : \( { x }^{ 2 }+{ y }^{ 2 }=1 \)

Now prove that: \( \frac { 1 }{ 1+{ x }^{ 2 } } +\frac { 1 }{ 1+{ y }^{ 2 } } +\frac { 1 }{ 1+xy } \ge \frac { 3 }{ 1+{ \left( \frac { x+y }{ 2 } \right) }^{ 2 } } \)

Note by Jolly Ghosh
1 year, 7 months ago

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put x and y as asin@ and acos@ and then solve it Abhishek Sharma · 1 year, 7 months ago

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@Abhishek Sharma Solve without using any kind of Trigonometrical topics and Jensen's Inequality. Use: AM, GM, HM, CS, Titu's Lemma or any other kind of inequality to solve. Jolly Ghosh · 1 year, 7 months ago

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