An algebra problem by Dipa Parameswara

Algebra Level 5

Let x,y,zx,y,z be all real numbers such that x+y+z=2x+y+z=2.

What is the minimum value of n=x2+7+y2+11+z2+13 n = \sqrt{x^{2}+7}+\sqrt{y^{2}+11}+\sqrt{z^{2}+13} ?

Give your answer to 3 decimal places.

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