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If a^2+b^2,a b+b c ,a n db^2+c^2 are in ...

If `a^2+b^2,a b+b c ,a n db^2+c^2` are in G.P., then `a ,b ,c` are in a. A.P. b. G.P. c. H.P. d. none of these

A

A.P.

B

G.P

C

H.P

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`a^(2)+b^(2),ab+bc,,b^(2)+c^(2)` are in G.P.
`rArr(ab+bc)^(2)=(a^(2)+b^(2))(b^(2)+c^(2))`
or `a^(2)b^(2)+b^(2)c^(2)+b^(2)c^(2)+2ab^(2)c=a^(2)b^(2)+a^(2)c^(2)+b^(2)c^(2)+b^(4)`
or `b^(4)+a^(2)c^(2)-2ab^(2)c=0`
or `(b^(2)-ac)^(2)=0`
or `b^(2)=ac`
Hence, a,b and c are in G.P.
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