Question: The arithmetic mean of a. b R is A(a, b) = (a + b)/2, and the geometric mean of a, b [0, )

The arithmetic mean of a. b ∈ R is A(a, b) = (a + b)/2, and the geometric mean of a, b ∈ [0, ∞) is G(a, b) = √ab. If 0 < a < b, prove that a < G{a, b) < A(a, b) < b. Prove that G(a, b) = A(a, b) if and only if a = b.

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