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# Symmetrical Minima. (TOMATO Subjective 33)

Problem: Let $$k$$ be a fixed odd positive integer. Find the minimum value of $$x^2 + y^2$$, where $$x,y$$ are non-negative integers and $$x+y=k$$.

Solution: We have $$y=k-x$$. Therefore we get an equation in $$x$$ where $$k$$ is a constant, precisely $$f(x) = x^2 + (k-x)^2$$.

To minimise, we differentiate $$f(x)$$ w.r.t $$x$$.

October 26, 2016

### 1 comment

1. This one is also pretty simple through Cauchy Schwartz