The AM between two positive numbers exceeds the GM by 5, and the GM exceeds the HM by 4. Then the numbers are
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Singhan Mahale
The A.M. between two positive numbers exceeds the GM by 5, and Gm exceed the H.M. by 4. Then the numbers are
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ANSWER
Given
A.M =5+GM -(1)
G.M =4+H.M - (2)
We know
G.M
2
=AM⋅HM
GM
2
=(5+GM)(GM−4)
GM
2
=5GM−20+GM
2
−4GM
∴GM=20
AM=25 (from (1))
ab
=20,
2
a+b
=25⇒a+b=50
⇒ab=400 …(3)
⇒(a−b)
2
=(a+b)
2
−4ab
=50
2
−4×400
=2500−1600
=900
∴a−b=
900
=30 …(4)
from (3) & (4)
a+b=50
a−b=30
______________
2a=80
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