Question

If A and G be the A.M and G.M between two positive number then the numbers are A + (A^2 – G^2)^1/2,  A – (A^2 – G^2)^1/2.

(a) True

(b) False

This question was addressed to me during an interview.

This intriguing question comes from Arithmetic and Geometric Mean topic in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

The correct choice is (a) True

To explain: The equation having its roots as given equation is

x^2 – 2Ax + G^2 = 0 which implies

x = A + (A^2 – G^2)^1/2,  A – (A^2 – G^2)^1/2.