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Question

Given that α,β,a,b are in A.P., α,β,c,d are in G.P. and α,β,e,f are in H.P. If b, d, f are in G.P., then βα6αβ(β4α4) equals to

A
23
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B
32
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C
43
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D
34
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Solution

The correct option is B 32
α,β,a,b are in A.P
b=a+3(βα)=3β2α
α,β,c,d are in G.P.
d=α(βα)3=β3α2
α,β,e,f are in H.P
1f=1α+3(1β1α)
f=αβ3α2β
Now since b, d, f are in G.P.
d2=bf
(β3α2)2=(3β2α)(αβ)3α2β
β5(3α2β)=α5(3β2α)
3αβ(β4α4)=2(β6α6)
32=β6α6αβ(β4α4)

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