Q9 of 176 Page 20

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

If a, b, c, d are in G.P, prove that :

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

If a, b, c are in G.P., prove that the following are also in G.P. :

a², b², c²

If a, b, c are in G.P., prove that the following are also in G.P. :

a³, b³, c³

If a, b, c, d are in G.P, prove that :(b + c) (b + d) = (c + a) (c + d)