Permutations And Combinations

Question

# If a be the A.M. and x, y be the two G.M.'s between b and c, show that

Solution

Since a is the A.M. between b and c

∴                                                   ...(i)
Since x, y are two G.M.'s between b and c

∴          b, x, y, c are in G.P.
Let r be the common ratio

L.H.S.  =

= bc (b + c) = bc(2a)                                 {By using (i)}
= 2abc =  R.H.S.
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