If a,b,c are in GP, prove that `(a^2-b^2)(b^2+c^2)=(b^2-c^2)(a^2+b^2)`.

If a,b,c are in G.P., then show that : (a^2-b^2)(b^2+c^2)=(b^2-c^2)(a^2+b^2)

If a, b, c, d are in GP, prove that (a^(2)-b^(2)), (b^(2)-c^(2)), (c^(2)-d^(2)) are in GP.

If a,b,c,d are in G.P.,prove that (a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P.and (1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P

If a, b, c are in GP, prove that (a^(2)+b^(2)), (ab+bc), (b^(2)+c^(2)) are in GP.

If a,b,c,d are in G.P.prove that: (a^(2)+b^(2)),(b^(2)+c^(2)),(c^(2)+d^(2)) are in G.P.(a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P.(1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P.(a^(2)+b^(2)+c^(2)),(ab+bc+cd),(b^(2)+c^(2)+d^(2))

If a,b,c are in G.P., then show that : a(b^2+c^2)=c(a^2+b^2)

If a,b,c are in G.P.,prove that: a(b^(2)+c^(2))=c(a^(2)+b^(2))A^(2)b^(2)c^(2)((1)/(a^(3))+(1)/(b^(3))+(1)/(c^(3)))=a^(3)+b^(3)+c^(3)((a+b+c)^(2))/(a^(2)+b^(2)+c^(2))=(a+b+c)/(a-b+c)(1)/(a^(2)-b^(2))+(1)/(b^(2))=(1)/(b^(2)-c^(2))(a+2b=2c)(a-2b+2c)=a^(2)+4c^(2)

If a, b, c are in GP, prove that a^(2), b^(2), c^(2) are in GP.

If a, b, c, d are in GP, prove that (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2) .

If a,b,c,d are in G.P.prove that: (i) quad (a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P. (i) (1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P.