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If one geometric mean G and two arithmet...

If one geometric mean `G` and two arithmetic means `A_1a n dA_2` be inserted between two given quantities, prove that `G^2=(2A_1-A_2)(2A_2-A_1)dot`

A

0

B

1

C

`-1.5`

D

`-2.5`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • If one geometric mean G and two arithmetic means A_(1)andA_(2) are inserted between two given quantities, then (2A_(1)-A_(2))(2A_(2)-A_(1))=

    A
    2G
    B
    G
    C
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    A
    n(a+b)
    B
    n/2 (a+b)
    C
    2n(a+b)
    D
    n/2 (a-b)

  • If n arithmetic means are inserted between two quantities a and b , then their sum is equal to :

    A
    `n(a+b)`
    B
    `n/2 (a+b)`
    C
    `2n(a+b)`
    D
    `n/2 (a-b)`

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