Y by
Given that
are positive real numbers satisfying the condition
,
find the maximum value of the expression:
![\[
P = \frac{1}{1+x^2} + \frac{1}{1+y^2} + \frac{z}{1+z^2}
\]](//latex.artofproblemsolving.com/4/e/6/4e6a6e3d1c959f8d16f08f7a8f842c20749fcef0.png)


find the maximum value of the expression:
![\[
P = \frac{1}{1+x^2} + \frac{1}{1+y^2} + \frac{z}{1+z^2}
\]](http://latex.artofproblemsolving.com/4/e/6/4e6a6e3d1c959f8d16f08f7a8f842c20749fcef0.png)
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