There's Only One Equation?

Algebra Level 3

x+1+y+z4=x+y+z2\large \sqrt{x+1} + \sqrt y + \sqrt{z-4} = \dfrac{x+y+z}2

x,yx,y and zz are real numbers satisfying the equation above. Find x+y+zx+y+z.


Courtesy: AMTI 2015
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