MathDB

19

Part of 2005 National Olympiad First Round

Problems(1)

P19 [Algebra] - Turkish NMO 1st Round - 2005

Source:

11/2/2013
What is the greatest real root of the equation x3−x2−x−13=0x^3-x^2-x-\frac 13 = 0?
<spanclass=′latex−bold′>(A)</span> 3−22<spanclass=′latex−bold′>(B)</span> 33−232<spanclass=′latex−bold′>(C)</span> 133−1<spanclass=′latex−bold′>(D)</span> 143−1<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ \dfrac{\sqrt {3} - \sqrt{2}}{2} \qquad<span class='latex-bold'>(B)</span>\ \dfrac{\sqrt [3]{3} - \sqrt[3]{2}}{2} \qquad<span class='latex-bold'>(C)</span>\ \dfrac 1{\sqrt[3] {3} - 1} \qquad<span class='latex-bold'>(D)</span>\ \dfrac 1{\sqrt[3] {4} - 1} \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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