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The G.M. of two positive numbers is 6. T...

The G.M. of two positive numbers is 6. Their arithmetic mean A and harmonic mean H satisfy the equation `90A+5H=918`, then A may be equal to

A

`(1)/(5)`

B

5

C

`(5)/(2)`

D

10

Text Solution

Verified by Experts

The correct Answer is:
A, D
`:.G=6` and `G^(2)=AH`
`implies H=(36)/(A)`
Given, `90A+5H=918`
`implies 90A+5xx(36)/(A)=918" " implies 5A+(10)/(A)=51`
`implies 5A^(2)-51A+10=0" " implies (A-10)(5A-1)=0`
`:.A=10,(1)/(5)`
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