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If the A.M. between two numbers exceeds ...

If the A.M. between two numbers exceeds their G.M. by 2 and the GM. Exceeds their H.M. by 8/5, find the numbers.

Text Solution

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A-G=2 (1)
G-H=8/5 (2)
`G^(2)=AH=(G+2(G-8//5)`
or G=8
or ab=64 (3)
From (1), we get
A=10
`rArr` a+b=20 (4)
Solving (3) and (4), we get a=4 and b=16
or a=16 and b=4
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