Question

Find H.M. of two positive numbers A.M. and G.M. are 15/2 and 6 respectively​

Answer 1

Given:

A.M and G.M are 15/2 and 6 respectively.

To Find:

The H.M of two positive integers.

Solution:

H.M.(harmonic mean) =?

A.M.(arithmetic mean) = 15/2

G.M.(geometric mean) = 6

Now, using the formula,

GM² = AM×HM

So, we already have the values of GM and HM, substituting the same in the formula.

⇒ GM² = AM×HM

⇒ (6)² = 15/2 × HM

Now, we know that 36 is the square of 6. And the shift value of AM to the left to find the value of HM.

⇒ 36×2/15 = HM

dividing the given value,

⇒ we get 12×2/5 = HM

⇒ 24/5 = HM

This cannot be further divided. so, HM = 24/5

Therefore, the HM is 24/5 of two positive numbers AM and GM are 15/2 and 6 respectively.