Inequality

IIT JEE 2015 Guidance › Algebra questions › Inequality

\hspace{-16}$If $\bf{xy=1}$ and $\bf{x,y\in\mathbb{R}}$ and satisfy the Relation $\bf{\left\{(x+y)^2+4\right\}.\left\{(x+y)^2-2\right\}\geq \mathbb{A}.(x-y)^2}$\\\\ Then $\bf{\mathbb{A}}$ is

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Shubhodip ·2012-05-20 07:31:43

something like \frac{8 \sqrt{17} + 24}{ \sqrt{17} - 1} ?

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rahul ·2012-05-20 15:05:27

let (x + y)² = m => (x - y)² = m - 4

given, (m + 4)(m - 2) > A (m - 4)

=> m² + 2m - 8 - Am + 4A > 0

=> m² + m (2 - A) - 8 + 4A > 0

clearly, a = coeff. of m > 1

=> D = 0

=> (2 - A)² - 4 (4A - 8) = 0

=> 4 + A² - 4A - 16A + 32 = 0

=> A² - 20A + 36 = 0

=> A = 18 or 2 ???????

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man111 singh ·2012-05-20 18:18:26

Thanks Rahul

Answer Given is = 18

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Inequality

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