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.


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