Question

find GM of two positive number whose A.M and H.M are 75 and 48

Answer 1

Let x,y be two numbers.

AM = (x + y)/2, GM = √xy, HM = (2xy/x + y).

⇒ AM * HM = (GM)²

According to Question,

AM = 75 and HM = 48.

⇒75 * 48 = (GM)²

⇒ 3600 = (GM)²

⇒ GM = 60

Hence,

Geometric mean,G.M of the numbers = 60

Answer 2

Given,

A.M. of two positive numbers = 75

H.M. of the two positive numbers = 48

To find,

The G.M. of the two positive numbers.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

The Arithmetic Mean (A.M.), Geometric Mean (G.M.), and Harmonic Mean (H.M.) of a set of data is related as follows:

The product of the arithmetic mean(A.M.) and harmonic mean(H.M.) is equal to the square of the geometric mean(G.M.), that is,

(A.M.) × (H.M.) = (G.M.)^2

{Statement-1}

Now, according to the question;

(A.M.) × (H.M.) = (G.M.)^2

=> (75) × (48) = (G.M.)^2

=> (G.M.)^2 = 25×3×3×16 = 5×5×3×3×4×4

=> (G.M.)^2 = (3×4×5)^2

=> G.M. = 3×4×5 = 60

=> G.M. = 60

Hence, the G.M. of the two positive numbers is equal to 60.