If one geometric G and two arithmetic means A1 and A2 are inserted between two distinct positive numbers, then 2A1−A2G2A2−A1G equal to 

If one geometric G and two arithmetic means A1 and A2 are inserted between two distinct positive numbers, then 2A1A2G2A2A1G equal to 

  1. A

    0

  2. B

    1

  3. C

    -1.5

  4. D

    -2.5

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    Solution:

    Let two distinct positive numbers be a and b.

    We have

                                2A1A2=2(a+d)(a+2d)=a

    and    2A2A1=2(bd)(b2d)=b

    Thus, 2A1A2G2A2A1G=abG2=1

     

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