If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A ± √((A + G)(A – G)).

Question

TextRelationship Between Arithmetic Mean and Geometric Mean

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If A.M. and G.M. of two positive numbers a and b are 10 and 8, respectively, find the numbers.

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio (3 + 2√2) : (3 – 2√2).

If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.

The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that a : b = (m + √(m2 – n2)) : (m – √(m2 – n2)).