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- Not so easy optimization of variables? 4 answers
What is the maximum value of $x^2+y^2$, where $(x,y)$ are solutions to:
Note: Calculus is not allowed. I tried everything I could but whenever I got for example or $x^2+y^2=f(y)$ or $f(x)$ the function $f$ would always be a concave up parabola, so I could not find a maximum for either variable. And by the way I know that you can solve for $x$ and $y$ using the quadratic formula and get $4$ different solutions but I am looking for less messy way. I've asked this question before, but I didn't get the nice answer I wanted. Thanks.
This question came from a math competition from the Math Honor Society, Mu Alpha Theta.