if `(a^(2) + c^(2))`, `(ab + cd)` and `(b^(2) + d^(2))` are in continued proportion, prove that `a`, `b`, `c` and `d` are in proportion.

If a,b,c and d are in proportion, then

if a + c = mb and (1)/(b)+ (1)/(d) = (m)/(c) , prove that a , b , c and d are in proportion.

If a + c = b e and 1/b + 1/d = e/c , Prove that : a,b,c and d are in proportion.

Quantities a , 2 , 10 and b are in continued proportion, find the values of a and b .

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

(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)) .

If a, b, c are in continued proportion, then which of the following to follow.

Factorise 2(ab + cd) - a^(2) - b^(2) +c^(2) +d^(2)

Factorise : a^(2) + b^(2) - c^(2) - d^(2) + 2ab - 2cd