Question

3. If a, b, c, d are in GP, prove that
(i) (b + c)(b + d) = (c + a)(c + d)​

Answer 1

Answer:

see below

Step-by-step explanation:

a, b, c, d are in GP

b/c = c/d

b/c +1 = c/d+1

b+c/c = c+d/d

b+c/c+d= c/d ----(1)

now a/c = b/d

a/c +1 = b/d+1

a+c/c = b+d/d

a+c/b+d = c/d ----(2)

from (1) & (2)

b+c/c+d = a+c/b+d

hence (b+c)(b+d) = (c+a)(c+d)