Question

57.
If AM of two numbers is 17 and GM is 15, find HM.
14 MIN

Answer 1

Given:

A.M. of two numbers is 17

G.M. of the same two numbers is 15

To find:

H.M.

Solution:

Let's assume "a" and "b" are the two numbers

So, we have

$\boxed{\bold{Arithmatic \:Mean\:of\: a\:\&\:b : \Rightarrow \frac{a+b }{2} }}\\\\\boxed{\bold{Geometric \:Mean\:of\: a\:\&\:b : \Rightarrow \sqrt{ab} }}\\\\\boxed{\bold{Harmonic \:Mean\:of\: a\:\&\:b : \Rightarrow \frac{2ab }{a+b} }}$

We can conclude,

$\bigstar\sim\boxed{\boxed{\bold{G.M.^2 = A.M. \times H.M.}}}\sim\bigstar$

Now, substituting the given values of A.M. and G.M.in the formula above, we get

$15^2 = 17 \times H.M.$

$\implies 225 = 17 \times H.M.$

$\implies H.M. = \frac{225}{17}$

$\implies \bold{H.M. = 13.23}$

Thus, the value of H.M. is 13.23.

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