If ` a^2+2bc ,b^2+2ca, c^2+2ab` are in A.P. then :-

Options

A. `(a-b)(c-a),(a-b)(b-c),(b-c)(c-a)` are in A.P
B. b-c,c-a,a-b are in H.P
C. a+b,b+c,c+a are in H.P
D. `a^2,b^2,c^2` are in H.P

Answer

A, B

Explanation

`a^(2)+2bc,b^(2)+2ca,c^(2)+2b`
`thereforeab+bc+ca-a^(2)-2bc,ab+bc+ca-b^(2)-2ca`,
`ab+bc+ca-c^(2)-2ab` are in A.P.
`rArr(c-a)(a-b),(a-b)(b-c),(b-c)(c-a)` are in A.P.
`((c-a)(a-b))/((a-b)(b-c)(c-a)),((a-b)(b-c))/((a-b)(b-c)(c-a)),`
`((b-c)(c-a))/((a-b)(b-c)(c-a))` are in A.P.
`rArr b-c,c-a,a-b` are in H.P.