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)))`

If (a)/(b) = (c)/(d) , show that : (a + b) : (c + d) = sqrt(a^(2) + b^(2)) : sqrt(c^(2) + d^(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 (7a + 8b)/( 7c + 8d) = (7a - 8b)/(7c - 8d), prove that : (i) a:b=c:d (ii) (4a - 5b)/(4c - 5d)= (3a + 4b)/(3c + 4d)

If a : b = c : d , prove that : (6a + 7b) (3c - 4d) = (6c + 7d) (3a - 4b) .

((144)^(1/2)+(256)^(1/2))/(3^2-2) = (A) 8 (B) 4 (C) -4 (D) -8

If (7a + 8b)/( 7c + 8d) = (7a - 8b)/(7c - 8d), prove that : a:b= c:d

If (a)/(2b) = (c )/(d) = (e )/(3f) , then the value of (2a^(4)b^(2)+3a^(2)c^(2)-5e^(4)f)/(32b^(6)+12b^(2)d^(2)-405f^(5)) is

In Fig. , A D=4c m , B D=3c m and C B=12 c m , find cottheta . (a) (12)/5 (b) 5/(12) (c) (13)/(12) (d) (12)/(13) (

If (7a + 8b) (7c - 8d) = (7a - 8b) (7c + 8d) : prove that a : b = c : d .