# 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.