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P19 [Algebra] - Turkish NMO 1st Round - 2013

Source:

April 20, 2013
analytic geometry

Problem Statement

What is the minimum value of x2−4x+7−22+x2−8x+27−62\sqrt {x^2 - 4x + 7 - 2\sqrt 2} + \sqrt {x^2 - 8x + 27 - 6\sqrt 2} where xx is a real number?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 32<spanclass=′latex−bold′>(C)</span> 1+2<spanclass=′latex−bold′>(D)</span> 22<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 2 \qquad<span class='latex-bold'>(B)</span>\ 3\sqrt 2 \qquad<span class='latex-bold'>(C)</span>\ 1 + \sqrt 2 \qquad<span class='latex-bold'>(D)</span>\ 2\sqrt 2 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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