If `pv^(a)=c` (a and c are costants) then show that `v^(2)(d^(2)p)/(dv^(2))=a(a+1)p`

pv^a=c (a and c are constants) then show that v^2(d^2p)/(dv^2)=a(a+1)p .

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

If p^(2)=a^(2)cos^(2)theta+b^(2)sin^(2)theta , show that, p+(d^(2)p)/(d theta^(2))=(a^(2)b^(2))/(p^(3)) .

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

If a, b, c are In A.P., then show that, a^(2)(b+c), b^(2)(c+a), c^(2)(a+b) are in A.P. (ab+bc+ca != 0)

If a, b, c and d are in G.P., show that, a^(2) + b^(2), b^(2) + c^(2), c^(2) + d^(2) are in G.P.

If a, b, c, d are in A.P. and a, b, c, d are in G.P., show that a^(2) - d^(2) = 3(b^(2) - ad) .

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

If a ,b ,c ,and d are in H.P., then find the value of (a^(-2)-d^-2)/(b^(-2)-c^-2) .

If a, b, c are In A.P., then show that, (1)/(b c), (1)/(c a), (1)/(a b) are in A.P.