\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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3 Answers
36let (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 ???????
