Question

if alpha beta gamma are the geometric means between CA AB AB BC CA respectively then a b c are in AP then find Alpha square beta square gamma square are in
pls don't post unnecessary answer

Answer 1

Step-by-step explanation:

By given condition

α

2

=a

2

bc,β

2

=b

2

ca,γ

2

=c

2

aband2b=a+c

α

2

,β

2

,γ

2

will be in A.P. if a

2

bc,b

2

ca,c

2

ab

are in A.P. or a,b,c are in A.P. which is true.

Again β+γ,γ+α,α+β will be in H.P. if

β+γ

1

,

γ+α

1

,

α+β

1

or

γ+α

1

−

β+γ

1

=

α+β

1

−

γ+α

1

or

β−γ

β−α

=

α+β

γ−β

orβ

2

−α

2

=γ

2

−β

2

or α

2

,β

2

,γ

2

are in A.P. Which we have already proved.