Question

The harmonic mean of two numbers is 4.Their arithmetic mean is A and geometric mean is G.If G satisfies 2a + G^2 = 27 then the numbers are​

Answer 1

Answer:

3 and 6

Step-by-step explanation:

Let no. be x and y

Then, 2xy/(x+y) = 4

or, 2(x+y)=xy

Also, 2A+G^2=27

or, 2*(x+y)/2 + (√xy) ^2 = 27

or, x+y+xy=27

or, 3xy/2=27

or, xy=18

Then, x+y = 18/2 = 9

And, (x-y)^2 = (x+y)^2 - 4xy = 81-72 = 9

or, x-y =3 or -3

x= 6,y=3

or

x=3,y=6