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If $x^2+y^2=1$, what is the largest possible value of $|x|+|y|$? Thanks!

 Feb 21, 2021
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Equality is achieved when \(x^2 = y^2 = \frac{1}{2}\).

 

\(\max({|x|+|y|}) = \frac{\sqrt{2}}{2} \cdot 2 = \boxed{\sqrt{2}}\)

 Feb 21, 2021

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