(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 agoConstruct a quadratic in x such that A.M. of its roots is A and G.M. is G.
Find the geometric means of the following pairs of numbers:
(i) 2 and 8
(ii) a3b and ab3
(iii) –8 and –2
Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).