Question

find the GM where AM and HM are 12 and 3 ​

Answer 1

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step-by-step explanation:

Let the two positive numbers be 'x' and 'y'.

Now,

it is given that,

Arithmetic mean, A.M = 12

=> x + y = 12 × 2

=> x + y = 24..................(i)

Now,

given that,

Harmonic mean, H.M = 3

doing cross multiplication,

we get,

Taking L.C.M of denominators and simplifying,

we get,

But, from eqn (i),

(x+y) = 24,

so putting the value,

we get,

On cross-multiplication,

we get,

But,

we know that,

Geometric mean, G.M of two numbers is the square root of their product.

so,

G.M of 'x' and 'y' is

But,

xy = 36

therefore,

G.M =

=> G.M = 6

Hence,

Geometric mean,G.M of the numbers = 6