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2012 Kazakhstan National Olympiad, 3

Let $ a,b,c,d>0$ for which the following conditions:: $a)$ $(a-c)(b-d)=-4$ $b)$ $\frac{a+c}{2}\geq\frac{a^{2}+b^{2}+c^{2}+d^{2}}{a+b+c+d}$ Find the minimum of expression $a+c$

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