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

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

If a,b,c,d are in continued proportion then show that abcd(1/a+1/b+1/c+1/d)^2 = (a+b+c+d)^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 continued proportion then show that bc(1/a+1/b+1/c+1/d) = a+b+c+d .

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

(i) If a , b , c are in continued proportion, show that : (a^(2) + b^(2))/(b(a+c)) = (b(a + c))/(b^(2) + c^(2)) . (ii) If a , b , c are in continued proportion and a(b - c) = 2b , prove that : a - c = (2(a + b))/(a) . (iii) If (a)/(b) = (c)/(d) show that : (a^(3)c + ac^(3))/(b^(3)d +bd^(3)) = ((a + c)^(4))/((b + d)^(4)) .