First slide

Means - A.M/G.M/H.M

Question

The harmonic mean of two numbers is 4. Their arithmetic mean is A and geometric mean is G. If G satisfies $2 A + G^{2} = 27$ then the numbers are

Moderate

A

1, 13
B

9, 12
C

3, 6
D

4, 8

Solution

$\frac{2 a b}{a + b} = 4, \frac{a + b}{2} = A \sqrt{a b} = G 2 A + G^{2} = 27 \Rightarrow a + b + a b = 27 \Rightarrow a + b + 2 (a + b) = 27 \Rightarrow a + b = 9 \Rightarrow a b = 18 \Rightarrow t h e n u m b e r s a r e 3, 6$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App