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If A and G be the AM and GM between two ...

If A and G be the AM and GM between two positive no.'s ; then the numbers are `Apmsqrt(A^2-G^2)`

A

` A pm (A^(2)-G^(2))`

B

`sqrt(A)pm sqrt(A^(2)-G^(2))`

C

` A pm sqrt((A=G)(A-G))`

D

` (A pm sqrt((A+G)(A-G)))/2`

Text Solution

Verified by Experts

The correct Answer is:
c
Let the two numbers be a and b
` :. AM = (a+b)/2 = A" "` (i)
` :. GM = sqrt(ab) = G rArr G^(2) =ab" " ` …(ii)
Now, `(a-b)^(2) = (a+b)6(2) -4ab = (2A)^(2) -4G^(2) = 4 (A^(2)-G^(2))`
` rArr a-b = pm 2 sqrt((A+G)(A-G))" "` …(iii)
On solving Eqs. (i) and (ii) , we get
` a = A pm sqrt((A+G)(A-G))`
and ` b = A pm sqrt((A+G)(A-G))`
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