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Wednesday, August 19, 2009

KBB2 Problem 9

Find the maximum $k$ such that

$\displaystyle (a^4 + b^4+c^4+d^4) + 4kabcd \geq \frac{k+1}{4}(a^2+b^2+c^2+d^2)^2$

always holds for $a,b,c,d$ positive reals.

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