If `a^2+b^2,a b+b c` and `b^2+c^2` are in G.P., then `a ,b ,c` are in

Options

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

Answer

B

Explanation

Given, `a^2+b^2,ab+bc`, and `b^2+c^2`
are in G.P.


Geometric mean relation for this:


`(ab+bc)^2=(a^2+b^2)(b^2+c^2)`


`a^2b^2+b^2c^2+2ab^2c=a^2b^2+b^4+a^2c^2+b^2c^2`


`2ab^2c=b^4+a^2c^2`


`b^4-2ab^2c+a^2c^2=0`


`(b^2-ac)^2=0`



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