Question

If a-b,b-c,c-a are in GP, then find the relation among a,b,c​

Answer 1

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Answer 2

Since they are in GP

$b - c = \sqrt{((a - b} )(c - a)) \\ squaring \: on \: both \: sides \\ ( b- c) ^{2} = (a - b)( c-a ) \\ {b}^{2} - 2bc + {c}^{2} =ac - { a}^{2} -bc + ab \\ { a}^{2} + {b}^{2} + {c}^{2} = ab+ bc+ ac$