If a, b, c are in G.P., show that
`a^(2)b^(2)c^(2)((1)/(a^(3))+(1)/(b^(3))+(1)/(c^(3))) = a^(3) + b^(3) + c^(3)`.

If a,b,c are in G.P then show that a^2b^2c^2(1/a^3+1/b^3+1/c^3)=a^3+b^3+c^3 .

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 ( 1/ a ^ 3 +1/ b ^ 3 ​ +1/ c ^ 3 ​ )=a ^ 3 +b^ 3 +c^ 3 .

If a,b,c,d are in G.P.then prove that (a^(3)+b^(3))^(-1),(b^(3)+c^(3))^(-1),(c^(3)+d^(3))^(-1) are also in G.P.

If a,b,c are in G.P. then show that :sum{log_(a)((b)/(c))}^(-1)=-3{log_(b)((c)/(a))}^(-1)

If a, b, c be in continued proportional, then prove that a^2 b^2 c^2 (1/a^3 + 1/b^3+1/c^3) =a^3 +b^3+c^3

If a,b,c, are in continued proportion then prove that a^2b^2c^2(1/a^3+1/b^3+1/c^3)= a^3+b^3+c^3 .

If b is the geometric mean of a and c, then show that a^2 b^2 c^2 [1/a^3 +1/b^3 +1/c^3] =a^3 +b^3 +c^3 .