#### Question :

If a,b,c, are in G.P. and x,y respectively arithmetic means between a,b and b,c then prove that1/x +1/y =2/bSubmitted on 10/7/2024 | Answered by Vandana Rana#### Answer :

a,b,c are in G.P(given)b

^{2}=ac

x is A.M. of a,b (given)

x=(a+b)/2

1/x=2/(a+b).......(1)

y is AM.of b ,c (given)

y=(b+c)/2

1/y =2/(b+c).........(2)

Adding (1) and (2)

1/x+1/y =2/(a+b) +2/(b+c)

=2[(b+c+a+b)/(ab+ac+b

^{2}+bc)]

=2[(2b+c+a)/(2b

^{2}+ab +bc)]

=2/b[(2b+c+a)/(2b+c+a)]

=2/b