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

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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