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P20 [Algebra] - Turkish NMO 1st Round - 2002

Source:

August 10, 2014

Problem Statement

Which of the following cannot be equal to x2+y2x^2+y^2, if x2+xy+y2=1x^2 + xy + y^2 = 1 where x,yx,y are real numbers?
<spanclass=′latex−bold′>a)</span> 12<spanclass=′latex−bold′>b)</span> 12<spanclass=′latex−bold′>c)</span> 2<spanclass=′latex−bold′>d)</span> 3−3<spanclass=′latex−bold′>e)</span> None of above <span class='latex-bold'>a)</span>\ \dfrac{1}{\sqrt 2} \qquad<span class='latex-bold'>b)</span>\ \dfrac 12 \qquad<span class='latex-bold'>c)</span>\ \sqrt 2 \qquad<span class='latex-bold'>d)</span>\ 3-\sqrt 3 \qquad<span class='latex-bold'>e)</span>\ \text{None of above}
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