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Turkish NMO First Round - 2012 Problem - 03 {Algebra}

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July 1, 2012

Problem Statement

Which one satisfies the equation 6+x3+6−x3=33\sqrt[3]{6+\sqrt{x}} + \sqrt[3]{6-\sqrt{x}} = \sqrt[3]{3} ?
<spanclass=′latex−bold′>(A)</span> 27<spanclass=′latex−bold′>(B)</span> 32<spanclass=′latex−bold′>(C)</span> 45<spanclass=′latex−bold′>(D)</span> 52<spanclass=′latex−bold′>(E)</span> 63 <span class='latex-bold'>(A)</span>\ 27 \qquad <span class='latex-bold'>(B)</span>\ 32 \qquad <span class='latex-bold'>(C)</span>\ 45 \qquad <span class='latex-bold'>(D)</span>\ 52 \qquad <span class='latex-bold'>(E)</span>\ 63
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