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

Options

A. A.P.
B. G.P
C. H.P
D. none of these

Answer

B

Explanation

`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.