Question

The arithmetic mean and geometric mean between two numbers is

related as A.M : G.M= 5:4. If the difference between geometric mean

and harmonic mean is – 4/5 then find the two numbers.​

Answer 1

Answer:

First Part,

Let a and b be two numbers.

According to question,

2

a+b

=5⟹a+b=10.....................(i)

ab

=4⟹ab=16.........................(ii)

Now, H.M between a and b=

a+b

2ab

=

10

2×16

=

5

16

Or,

Let a be first term and d be the common difference of corresponding A.P.

a+2d

1

=1.............(i)

a+4d

1

=−5....................(ii)

Solving both equations , we get

a=7 and d=−3

Now, t

10

=

a+9d

1

=

7+9×(−3)

1

=−

20

1

Answer 2

Answer:

ANSWER :

* First Part,

Let a and b be two numbers.

According to question,

2

a+b

=5⟹a+b=10.....................(i)

ab

=4⟹ab=16.........................(ii)

Now, H.M between a and b=

a+b

2ab

=

10

2×16

=

5

16

Or,

Let a be first term and d be the common difference of corresponding A.P.

a+2d

1

=1.............(i)

a+4d

1

=−5....................(ii)

Solving both equations , we get

a=7 and d=−3

Now, t

10

=

a+9d

1

=

7+9×(−3)

1

=−

20

1