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Determine the coldest point of the plane

Source: Finnish Mathematics Competition 2009, Final Round - P1

November 16, 2011
linear algebramatrixalgebra proposedalgebra

Problem Statement

In a plane, the point (x,y)(x,y) has temperature x2+y2āˆ’6x+4yx^2+y^2-6x+4y. Determine the coldest point of the plane and its temperature.
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