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Turkish NMO First Round - 2012 Problem - 11 {Algebra}

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July 1, 2012

Problem Statement

The number of real quadruples (x,y,z,w)(x,y,z,w) satisfying x3+2=3y,y3+2=3z,z3+2=3w,w3+2=3xx^3+2=3y, y^3+2=3z, z^3+2=3w, w^3+2=3x is
<spanclass=′latex−bold′>(A)</span> 8<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 1<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ 8 \qquad <span class='latex-bold'>(B)</span>\ 5 \qquad <span class='latex-bold'>(C)</span>\ 3 \qquad <span class='latex-bold'>(D)</span>\ 1 \qquad <span class='latex-bold'>(E)</span>\ \text{None}
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