# Nope, not $$x=y=z$$

Algebra Level 5

Let $$a, b, c$$ be positive reals so that $$3ab+bc+2ca=6$$. Find the maximum value of

$\frac { 1 }{ { a }^{ 2 }+1 } +\frac { 4 }{ { b }^{ 2 }+4 } +\frac { 9 }{ { c }^{ 2 }+9 }$