Prove that $(a b + x y) (a x + b y) \geq 4 a b x y$ .

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Solution

$a b + x y \geq 2 \sqrt{a b x y}$ .............(1)
[By A.M - G.M inequality}
$a x + b y \geq 2 \sqrt{a b x y}$ ..............(2)
Multiplication of above equations
$(a b + x y) (a x + b y) \geq 4 a b x y$

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