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If one A.M., A and tow geometric means G...

If one A.M., `A` and tow geometric means `G_1a n dG_2` inserted between any two positive numbers, show that `(G1 2)/(G_2)+(G2 2)/(G_1)=2Adot`

Text Solution

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Since two geometric means are inserted between `a^3` and `b^3`
that means it has four terms as,
`a^3,a^3r,a^3r^2,b^3`
So, `b^3 `is the fourth term of that GP.
So `=>a^3r^3=b^3`
`=>r=b/a`
now `G_1` is the second term
and `G_2` is the third term so,
...
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Knowledge Check

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    B
    A
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    3A
    D
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