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a,b,c are in ap , b,c,a are in hp prove that c,a,b are in gp

a,b,c are in ap , b,c,a are in hp prove that c,a,b are in gp

Grade:11

2 Answers

Arun
25750 Points
6 years ago
a,b,c are in A.P.
Hence
2b = a+ c
 
Now, b,c,a are in hp
Hence
C= 2a*b/(a+b)
Put 2b = a+ c in the above equation
a*c + b* c = a(a+ c)
a2 = bc
Hence we can say
c,a,b are in G.P.
Shailendra Kumar Sharma
188 Points
6 years ago
a,b,c in APThat means 2b =a +cb,c,a in HPManas 2/c = 1/b+1/aNow c=2ab/(a+b)c=ab/{(a+b)/2}c= ab/cc^2 = abSo a,b,c are in GP

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