Question

If a, b, c are in AP and
a², b², c² be in HP. Then Prove
that -a/2 b, c are in GP or else a=b=c​

Answer 1

Answer:

Byavatar

Dhruma Khun

Step-by-step explanation:

Let b=ar and c=ar  

2

, where r is common ratio  

Then,

a+b

1

​  

=  

a+ar

1

​  

=  

a(1+r)

1

​  

,  

2b

1

​  

=  

2ar

1

​  

,  

and  

(b+c)

1

​  

=  

ar(1+r)

1

​  

 

∴  

(a+b)

1

​  

+  

(b+c)

1

​  

=  

a(1+r)

1

​  

+  

ar(1+r)

1

​  

=  

ar(1+r)

(1+r)

​  

=  

ar

1

​  

=2×(  

2b

1

​  

). .... A.M.

Hence,  

(a+b)

1

​  

,  

2b

1

​  

,  

(b+c)

1

​  

 are in AP.

Answer Byavatar

Dhruma Khun