If a, b, c, d are in G.P, prove that :
(b + c) (b + d) = (c + a) (c + d)
a, b, c, d are in G.P.
Therefore,
bc = ad … (1)
b2 = ac … (2)
c2 = bd … (3)
LHS = b2 + bd + bc + cd
⇒ LHS = ac + bd + bc + cd {on substituting value of b2 } …(1)
RHS = c2 + cd + ac + ad
⇒ RHS = bd + cd + ac + bc {putting value of c2} …(2)
From equation 1 and 2 we can say that –
LHS = RHS Hence proved