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This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.

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How to minimize $(x-a)^2+(y-b)^2$ subject to $ \sqrt{a}+\sqrt{b}=\sqrt{2}$?

I am not sure if this is on-topic here, but I am trying. Let $x,y$ be positive real numbers. I am trying to find $$ \min_{\sqrt{a}+\sqrt{b}=\sqrt{2}}(x-a)^2+(y-b)^2$$ I tried using Mathematica for …