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If sum of the A.M. & G.M. of two positiv...

If sum of the `A.M. & G.M.` of two positive distinct numbers is equal to the difference between the number then numbers are in ratio :

A

`1:3`

B

`1:6`

C

`9:1`

D

`1:12`

Text Solution

Verified by Experts

The correct Answer is:
C
If "sum" of the `A.M.` & ……….
`(a+b)/(2)+sqrt(ab) = a-b`
`a+b+2sqrt(ab) = 2a-2b`
`(a-3b)^(2)= 4ab`
`a^(2)9b^(2) -10ab = 0`
`(a-9b)(a-b) = 0`
`a = 9b as a-b != 0`
`(a)/(b) = (9)/(1)`
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