If a, b, c are in HP then prove that `b^2(a-c)^2=2{c^2(b-a)^2+a^2(c-b)^2}`.

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

If a,b,c are in HP, then prove that (a+b)/(2a-b)+(c+b)/(2c-b)gt4 .

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

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

If a,b,c are in HP, then prove that sin ^(2) ""(A)/(2), sin ^(2) ""(B)/(2), sin ^(2) ""(C )/(2) are also in HP.

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

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 H.P., then (c^(2)(b-a)^(2)+a^(2)(c-b)^(2))/(b^(2)(a-c)^(2)) =