# Happy New Year 2016

Algebra Level 5

Let $$x,y,z$$ be positive reals such that $x^2+y^2+z^2=1$ if $axy+byz=\dfrac{\sqrt{a^2+b^2}}{2}$ for some positive real numbers $$a$$ and $$b$$, then the value of $$y$$ can be expressed as

$\large{\dfrac{A}{B\sqrt{C}} }$

where $$A$$ and $$B$$ are co-prime positive integers and a square free natural number $$C$$. Find $$A+B+C$$.

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