Problem 3

Algebra Level 5

$\frac{x^2}{x^2+yz+x+1}+\frac{y+z}{x+y+z+1}+\frac{1}{xyz+3}$

Given that $$x$$, $$y$$ and $$z$$ are non-negative numbers and $$x^2+y^2+z^2=2$$. Find the maximum value of the expression above.

This problem is in this set.

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