(a) Find the maximum value of 

given that x₁, x₂, . . . , x_n are positive numbers and x₁ + x₂ + ∙ ∙ ∙ + xn = c, where c is a constant.

(b) Deduce from part (a) that if x₁, x₂, . . . , xn are positive numbers, then

This inequality says that the geometric mean of n numbers is no larger than the arithmetic mean of the numbers. Under what circumstances are these two means equal?

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