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Turkey NMO 2008 1st Round - P31 (Algebra)

Source:

August 27, 2012
inequalities

Problem Statement

If the inequality ((x+y)2+4)((x+y)2−2)≥A⋅(x−y)2 ((x+y)^2+4)((x+y)^2-2)\geq A\cdot (x-y)^2 is hold for every real numbers x,yx,y such that xy=1xy=1, what is the largest value of AA?
<spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 14<spanclass=′latex−bold′>(C)</span> 16<spanclass=′latex−bold′>(D)</span> 18<spanclass=′latex−bold′>(E)</span> 20 <span class='latex-bold'>(A)</span>\ 12 \qquad<span class='latex-bold'>(B)</span>\ 14 \qquad<span class='latex-bold'>(C)</span>\ 16 \qquad<span class='latex-bold'>(D)</span>\ 18 \qquad<span class='latex-bold'>(E)</span>\ 20
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