If `a,b,c,d` are in proportion then prove that `sqrt((a^2+5c^2)/(b^2+5d^2))=a/b`

If a,b,c,d are in proportion, then prove that (a^2+ab+b^2)/(a^2-ab+b^2)=(c^2+cd+d^2)/(c^2-cd+d^2)

If a, b, c, d are in continued proportion, then prove that (b -c)^(2) + (c -a)^(2) + (b-d)^(2) = (a -d)^(2)

If a,b,c,d are in continued proportion then show that (b-c)^2+(c-a)^2+(b-d)^2= (a-d)^2 .

If a,b,c,d,e are in continued proportion,then prove that (ab+bc+cd+de)^(2)=(a^(2)+b^(2)+c^(2)+d^(2))(b^(2)+c^(2)+d^(2)+e^(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,d are in GP then prove that, (a^2-b^2), (b^2-c^2), (c^2-d^2) are in GP.

If a, b, c, d are in GP, then prove that 1/((a^(2)+b^(2))), 1/((b^(2)+c^(2))), 1/((c^(2)+d^(2))) are in GP.

If a,b,c,d are in continued proportion,prove that: a:b+d=c^(3):c^(2)d+d^(3).

If a,b,c,d are in geometric sequence then prove that (b-c)^(2) +(c-a)^(2) -(d-b)^(2)=(a-d)^2

if a , b , c and d are in proportion, prove that : (i) (a-b)/(c-d)= sqrt((3a^(2) + 8b^(2))/(3c^(2) + 8d^(2))) (ii) ((5a^(2) + 12c^(2))/(5b^(2) + 12d^(2))) = sqrt((3a^(4) - 7c^(4))/(3b^(4) - 7d^(4)))