If `a/b = b/c = c/d `, then show that ` (a - b)^(3) : (b - c)^(3) = a : d `.

If a/b = c/d ,then show that bd ((a+b)/b + (c+d)/d)^(2) = 4 (a + b) (c + d)

IF a=2/3 , b=(-5)/6 and c=7/d ,show that (a-b)-c ne a-(b-c)

If (a)/(b) = (c)/(d) , show that : (a + b) : (c + d) = sqrt(a^(2) + b^(2)) : sqrt(c^(2) + d^(2))

If a + b + c = 0 , show that a^(3) + b^(3) + c^(3) = 3abc The following are the steps involved in showing the above result. Arrange them in sequential order (A) a^(3) + b^(3) + 3ab (-c) = -c^(3) (B) (a + b)^(3) = (-c)^(3) (C) a + b + c = 0 rArr a + b = -c (D) a^(3) + b^(3) + 3ab (a +b) = -c^(3) (E) a^(3) + b^(3) + c^(2) = 3abc

if a : b = e : d , show that : 3a + 2b : 3a - 2b = 3c + 2d : 3c - 2d .

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

Given, (a)/(b) = (c)/(d) , prove that : (3a - 5b)/(3a + 5b) = (3c - 5d)/(3c + 5d)

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