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If `8` harmonic means are inserted between two numbes `a` and `b (altb)` such that arithmetic mean of `a` and `b` is `5/4` times equal to geometric me

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If `8` harmonic means are inserted between two numbes `a` and `b (altb)` such that arithmetic mean of `a` and `b` is `5/4` times equal to geometric mean of `a` and `b` then `((H_(8)-a)/(b-H_(8)))` is equal to
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`(a+b)/2=5/4sqrt(ab)`
`impliesa/b=1/4`
`(H_(8)-a)/(a-H_(8))=8xxa/b=8xx1/4=2`
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