Olympiad problem

Algebra Level 5

(x+y+z)2(1x+1y+1z)\large (x+y+z)^2 \left (\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z} \right)

Given that 12x,y,z1\dfrac12 \leq x,y,z\leq 1 , find the sum of the minimum and maximum value of the expression above.

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