Question

if the arithmetic and harmonic mean between two numbers are 27 and 12 respectively, then find their geometric mean​

Answer 1

Answer and Step-by-step explanation in attachment.

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Answer 2

The geometric mean between two numbers would be 18

Given

• arithmetic mean 27
• harmonic mean 12

To find

• geometric mean

Solution

we are provided with the Arithmetic mean and harmonic mean between two numbers and are asked to estimate the geometric mean of the same two numbers.

let a and b be the two numbers considered for the case,

Arithmetic mean of the two numbers would be,

(a+b)/2 = 27

or, a + b = 54

harmonic mean of the two numbers would be,

2ab/(a+b) = 12

or, 2ab/54 = 12

or, 2ab = 648

or, ab = 324

The geometric mean between the two numbers would be,

√(ab)

from above,

√(324)

or, 18

Therefore, the geometric mean between two numbers would be 18