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Turkey NMO 2010 1st Round - P31 (Algebra)

Source:

July 27, 2012

Problem Statement

For which pair (A,B)(A,B), x2+xy+y=Ayy−x=B x^2+xy+y=A \\ \frac{y}{y-x}=B has no real roots?
<spanclass=′latex−bold′>(A)</span> (1/2,2)<spanclass=′latex−bold′>(B)</span> (−1,1)<spanclass=′latex−bold′>(C)</span> (2,2)<spanclass=′latex−bold′>(D)</span> (1,1/2)<spanclass=′latex−bold′>(E)</span> (2,2/3) <span class='latex-bold'>(A)</span>\ (1/2,2) \qquad<span class='latex-bold'>(B)</span>\ (-1,1) \qquad<span class='latex-bold'>(C)</span>\ (\sqrt 2, \sqrt 2) \qquad<span class='latex-bold'>(D)</span>\ (1,1/2) \qquad<span class='latex-bold'>(E)</span>\ (2,2/3)
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