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If 34 and 16 are the Arithmetic Means and Geometric Means of two positive numbers respectively. Find the numbers.

Asked by Topperlearning User 7th October 2016, 12:23 PM
Answered by Expert
Answer:
Let the two numbers be m and n. Then
Arithmetic Mean = 34
⇒ (m + n)/2 = 34
⇒ m + n = 68
And
Geometric Mean = 16
√mn = 16
⇒ mn = 256 ............................... (i)
Therefore, (m-n)2= (m + n)2-4mn
⇒ (m – n)2 = (68)2-4(256) = 3600
⇒ m-n=plus-or-minus60............................... (ii)
On solving (i) and (ii), we get m = 64 and n = 4 with m-n=60 and

m=4 and n=64  with m-n=-60

So the numbers are 4 and 64
Answered by Expert 7th October 2016, 2:23 PM
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