Question

The Arithmetic mean and Harmonic mean of two postive numbers 24 and 6.What is the geometric mean of the two numbers a and b

Answer 1

Answer:

12

Step-by-step explanation:

given AM = 24 =(a+b)/2.

HM = 6= (2ab)/a+b.

now,

24=(a+b)/2

a+b=48 ----------------------------------eqn - 1

6=(2ab)/a+b

putting value of (a+b) we get

ab=144

a=144/b------------------eqn - 2

putting this in eqn 1 we get

b^2+144-48b

solving we get the value of  a &b

b = 12 & a = 12

now the GM = (a*b)^1/2

GM = (12*12)^1/2

GM=12