The arithmetic mean between two numbers is A and their geometric mean is G. Then the numbers are

\(\sqrt {{A^2} - {G^2} \pm A} \)

\( \pm \frac{1}{2}\sqrt {{A^2} - {G^2} + A} \)

\(A \pm \sqrt {{A^2} - {G^2}} \)

None of these

The arithmetic mean between two numbers is A and their geometric mean is G. Then the numbers are Correct Answer \(A \pm \sqrt {{A^2} - {G^2}} \)

Given:

Arithmetic mean = A

Geometric mean = G

Explanation:

Let the numbers be x and y

⇒ (x + y)/2 = A --(1)

⇒ √ (xy) = G

⇒ y = G²/x

Put the value of y in equation (1)

⇒ (x + (G²/x))/2 = A

⇒ x² + G² = 2Ax

⇒ x² + G²- 2Ax = 0

⇒ x = A ± √ (A² - G²)

Feb 20, 2025

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