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Question

If bc,2bx and ba are in H.P. then ax2,bx2 and cx2are in

A
A.P.
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B
G.P.
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C
H.P.
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D
None
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Solution

The correct option is B G.P.
bc,2bx and ba are in H.P.
2bx=2(bc)(ba)2b(a+c)x=2b2(b2abbc+ac)2b(a+c)=2(b2ac)2b(a+c)ax2=a(b2ac)2b(a+c)=(ab)2a+c2bbx2=b(b2ac)2b(a+c)=(ab)(cb)2baccx2=c(b2ac)2b(a+c)=(bc)2a+c2b(bx2)2=(ax2)(cx2)
so (ax2),(bx2),(cx2) are in G.P.

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