If `(b^2+c^2-a^2)/(2b c),(c^2+a^2-b^2)/(2c a),(a^2+b^2-c^2)/(2a b)` are in `A.P.` and `a+b+c=0` then prove that `a(b+c-a),b(c+a-b),c(a+b-c)` are in `A.P.`

If (b^(2) + c^(2) - a^(2))/(2bc), (c^(2) + a^(2) - b^(2))/(2ca), (a^(2) + b^(2) - c^(2))/(2ab) are in A.P. and a+b+c = 0 then prove that a(b+c-a), b(c+a-b), c(a+b-c) are in A.P.

If (b^(2)+c^(2)-a^(2))/(2bc), (c^(2)+a^(2)-b^(2))/(2ca) and (a^(2)+b^(2)-c^(2))/(2ab) are in A.P. then show that, a(b+c-a), b(c+a-c) and c(a+b-c) are also in A.P. [a+b+c != 0] .

If 1/a,1/b,1/c are in A.P. and a+b+cne0_2 prove that (b+c)/a,(c+a)/b,(a+b)/c are in A.P.

If a^(2),b^(2) and c^(2) are in AP then prove that (a)/(b+c),(b)/(c+a) and (c)/(a+b) are also in A.P.

If a, b, c are in A.P, then show that: \ b c-a^2,\ c a-b^2,\ a b-c^2 are in A.P.

Suppose that a, b, c are in A.P. Prove that a^2(b+c),b^2(c+a),c^2(a+b) are in A.P.

If a^2,b^2,c^2 are in A.P. prove that 1/(b+c),1/(c+a),1/(a+b) are in A.P.

If a^2,b^2,c^2 are in A.P. prove that 1/(b+c),1/(c+a),1/(a+b) are in A.P.

If (b-c)^(2), (c-a)^(2), (a-b)^(2) are in A.P. then prove that, (1)/(b-c), (1)/(c-a), (1)/(a-b) are also in A.P.

If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P., then prove that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.