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P12 [Algebra] - Turkish NMO 1st Round - 2003

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May 14, 2014

Problem Statement

How many real triples (x,y,z)(x,y,z) are there such that 4x21+4x2=y\dfrac{4x^2}{1+4x^2}=y, 4y21+4y2=z\dfrac{4y^2}{1+4y^2}=z, 4z21+4z2=x\dfrac{4z^2}{1+4z^2}=x ?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 6<spanclass=′latex−bold′>(D)</span> Infinitely many<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 2 \qquad<span class='latex-bold'>(B)</span>\ 4 \qquad<span class='latex-bold'>(C)</span>\ 6 \qquad<span class='latex-bold'>(D)</span>\ \text{Infinitely many} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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