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P36 [Algebra] - Turkish NMO 1st Round - 2001

Source:

April 23, 2014

Problem Statement

Let aa and bb be positive real numbers such that ab(a−b)=1ab(a-b)=1. Which of the followings can a2+b2a^2+b^2 take?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 22<spanclass=′latex−bold′>(D)</span> 11<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 2\sqrt 2 \qquad<span class='latex-bold'>(D)</span>\ \sqrt {11} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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