Problem 9

Algebra Level 4

xy+z+2x2+2y21+xy\large \dfrac{\sqrt{xy+z}+\sqrt{2x^2+2y^2}}{1+\sqrt{xy}}

Given that x,yx,y and zz are positive reals satisfying x+y+z=1x+y+z=1, find the minimum value of the expression above.


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