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P16 [Algebra] - Turkish NMO 1st Round - 2002

Source:

August 8, 2014

Problem Statement

Which of the following cannot be equal to x2+14xx^2 + \dfrac 1{4x} where xx is a positive real number?
<spanclass=latexbold>a)</span> 31<spanclass=latexbold>b)</span> 222<spanclass=latexbold>c)</span> 51<spanclass=latexbold>d)</span> 1<spanclass=latexbold>e)</span> None of above <span class='latex-bold'>a)</span>\ \sqrt 3 -1 \qquad<span class='latex-bold'>b)</span>\ 2\sqrt 2 - 2 \qquad<span class='latex-bold'>c)</span>\ \sqrt 5 - 1 \qquad<span class='latex-bold'>d)</span>\ 1 \qquad<span class='latex-bold'>e)</span>\ \text{None of above}