Problem 10

Algebra Level 5

\[\large \frac{1}{\sqrt[4]{a^2+b^2}}+\frac{1}{\sqrt[4]{b^2+c^2}}+\frac{1}{\sqrt[4]{c^2+a^2}}\]

Given that \(a,b,c\) are non-negative and at the same time two of three of the triple of numbers are non-zero and \(a+b+c=2\). Find the minimum value of the expression above.

Give your answer to two decimal places.

This problem is in this Set.


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