Permutations and Combinations

Permutations and Combinations

Question

If A and G be A.M. and G.M. between two positive numbers, then the numbers are

straight A plus-or-minus square root of straight A squared minus straight G squared end root.

Answer

Since the given numbers are the roots of the quadratic equation
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∴                               straight x equals fraction numerator 2 straight A plus-or-minus square root of 4 straight A squared minus 4 straight G squared end root over denominator 2 end fraction space equals space straight A plus-or-minus square root of straight A squared minus straight G squared end root

∴   Numbers are space space straight A plus square root of straight A squared minus straight G squared end root space space space and space space space straight A minus square root of straight A squared minus straight G squared end root

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