BALKAN-SL 2016 A5

Answer

Let $a, b, c$ and $d$ be real numbers such that $a+b+c+d=2$ and $a b+b c+c d+d a+a c+b d=0$ . Find the minimum value and the maximum value of the product $a b c d$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\min (a b c d)=-1 \text{ and } \max (a b c d)=\frac{1}{4}

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