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

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

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 are in G.P. then prove that (a^2+a b+b^2)/(b c+c a+a b)=(b+a)/(c+b)

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

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.

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

If a ,b, c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to

If a ,b ,c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to (a-d)^2 b. (a d)^2 c. (a+d)^2 d. (a//d)^2