Question

The HM of two numbers is 4. Their arithmetic mean A and geometric mean G satisfy the condition 2A + G^2= 27. find the nos.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The numbers are 6 and 3.

Step-by-step explanation:

Given,

Arithmetic mean is A ,Geometric mean is B and HM is 4

Let two number be a and b

According to question,

2ab/(a+b) = 4 and (a+b)/2 = A and ab=G²

Now,

2ab/(a+b) = 4

2G²/2A = 4

So, G²/A= 4

G²= 4A

Given 2A+G²= 27

2A+4A=27

6A=27

A=27/6

So,(a+b)/2=27/6

(a+b)=9......(1)

again 2ab/(a+b) = 4

2ab/9= 4

ab= 18.....(2)

Solve equation (1) and equation (ii) and get,

a=6 and b=3

The numbers and 6 and 3.