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Find max and min of f(x, y) = y-2x if (x^2+y^2)/(x+y) \leq 4

Source: Austrian Mathematical Olympiad 2003, Part 1, P2

June 18, 2011
inequalitiesgeometryinequalities proposed

Problem Statement

Find the greatest and smallest value of f(x,y)=y−2xf(x, y) = y-2x, if x, y are distinct non-negative real numbers with x2+y2x+y≤4\frac{x^2+y^2}{x+y}\leq 4.
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