Let α>0 be a fixed positive number and R={(x,y) ∈ R^2: 0≤y≤√α^2−x^2; 0≤x≤α}. Determine the value of α so that the mean value of the function f(x,y)=(x^2+y^2)^7/2 in the set R is equal to 1. Give your answer to two decimal places.

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