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`

Explanation

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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