Another symmetric inequality

Algebra Level 4

5x+4+5y+4+5z+4\large \sqrt{5x+4}+\sqrt{5y+4}+\sqrt{5z+4}

Let x,yx,y and zz be non-negative reals satisfying x+y+z=1x+y+z=1. Find the minimum value of the expression above.

Give your answer to 2 decimal places.


This problem was taken from Hanoi Pedagogic Highschool grade 10 selection test.
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