Friday, 1 March 2019

contest math - Inequality with sums and products

Let a,b,c,d positive real numbers such that

$a+b and
$(a+b)(c+d).
Prove that
(a+b)cd>(c+d)ab



Source: book on olympiads
I tried manipulating the given statements and i obtained
$3ab
To use this i would need to show that cd<3(a+b) but i am stuck.

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