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If one geometric mean G and two airthmetic mean A1, A2 are inserted between two numbers, then (2A1 – A2) (2A2 – A1) is equal to _______(a) 2G(b) G(c) G^2(d) None of the mentionedI had been asked this question in final exam.My enquiry is from Arithmetic and Geometric Mean topic in division Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer»

The correct option is (c) G^2

Explanation: Let a and B be TWO numbers then, G = (ab)^1/2, A1 = (2a+b)/3, A2 = (a+2b)/3, (2A1 – A2) = a, (2A2 – A1) = b, (2A1 – A2)(2A2 – A1) = G^2.



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