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Turkey NMO 2008 1st Round - P23 (Algebra)

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August 26, 2012

Problem Statement

If a2+b2+c2+d2−ab−bc−cd−d+25=0a^2+b^2+c^2+d^2-ab-bc-cd-d+\frac 25 = 0 where a,b,c,da,b,c,d are real numbers, what is aa?
<spanclass=′latex−bold′>(A)</span> 23<spanclass=′latex−bold′>(B)</span> 23<spanclass=′latex−bold′>(C)</span> 32<spanclass=′latex−bold′>(D)</span> 15<spanclass=′latex−bold′>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ \frac 23 \qquad<span class='latex-bold'>(B)</span>\ \frac {\sqrt 2} 3 \qquad<span class='latex-bold'>(C)</span>\ \frac {\sqrt 3} 2 \qquad<span class='latex-bold'>(D)</span>\ \frac 15 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
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