Question

13.
H. M. and A. M. of the two numbers are 3 and 4
respectively, find the numbers.​

Answer 1

Answer:

Step-by-step explanation:

Let the two numbers be p and q. Since the arithmetic mean of the two numbers is 4, thus we will take: -

= p+q)/2 = 4

= p+q = 8 … (1)

Now, since the harmonic mean of the two numbers is 3, therefore:

= 2/(1/p + 1/q) = 3

= 2/[(p+q)/pq] = 3

= 2pq/(p+q) = 3

= pq/(p+q) = 3/2 … (2)

Placing the value of p+q in equation (2), we take:

= pq/8/= 3/2

= pq = 16/3 … (3)

Therefore, the geometric mean of p and q is:

√pq = √16/3