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The geometric mean G of two positive num...

The geometric mean `G` 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

(A) `5/2`

B

(B) `10`

C

(C) `5`

D

(D) `1/5`

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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