Question

The AM between two positive numbers exceeds the GM by 5, and the GM exceeds the HM by 4. Then the numbers are

Answer 1

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