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

Asked by Sakshi | 1 year ago |  64

#### 1 Answer

##### Solution :-

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

Given that a, b, c are in GP.

By using the property of geometric mean,

b2 = ac

bc = ad

c2 = bd

Let us consider LHS: (b + c) (b + d)

Upon expansion we get,

(b + c) (b + d) = b2 + bd + cb + cd

= ac + c2 + ad + cd [by using property of geometric mean]

= c (a + c) + d (a + c)

= (a + c) (c + d)

= RHS

LHS = RHS

Hence proved.

Answered by Aaryan | 1 year ago

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