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The Arithmetic and Geometric Means of two positive numbers are 15 and 9 respectively. Find the numbers.

Asked by Topperlearning User 5th October 2016, 7:23 AM
Answered by Expert
Answer:

Let the two positive numbers be x and y. Then according to the problem,
(x + y)/2 = 15
or, x + y = 30 .................. (i)
and √xy = 9
or xy = 81
Now, (x-y)2= (x + y)2 - 4xy
= (30)2-4(81) 
= 576
= (24)2
Therefore,
x-y=± 24 .................. (ii)
Solving (ii) and (iii), we get,
2x = 54 or 2x = 6
x = 27 or x = 3
When x = 27 then y = 30-x
= 30-27
= 3
and when x = 27 then y = 30-x
= 30-3
= 27
Therefore, the required numbers are 27 and 3.
Answered by Expert 5th October 2016, 9:23 AM
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